Log in

Relevant bibliographies by topics / Lie algebras][Euclidean space

Contents

Journal articles
Dissertations / Theses
Books
Book chapters
Conference papers

Academic literature on the topic 'Lie algebras][Euclidean space'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Lie algebras][Euclidean space.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Lie algebras][Euclidean space"

1

Ait Ben Haddou, Malika, Saïd Benayadi, and Said Boulmane. "Malcev–Poisson–Jordan algebras." Journal of Algebra and Its Applications 15, no. 09 (August 22, 2016): 1650159. http://dx.doi.org/10.1142/s0219498816501590.

Full text

Abstract:

Malcev–Poisson–Jordan algebra (MPJ-algebra) is defined to be a vector space endowed with a Malcev bracket and a Jordan structure which are satisfying the Leibniz rule. We describe such algebras in terms of a single bilinear operation, this class strictly contains alternative algebras. For a given Malcev algebra [Formula: see text], it is interesting to classify the Jordan structure ∘ on the underlying vector space of [Formula: see text] such that [Formula: see text] is an MPJ-algebra (∘ is called an MPJ-structure on Malcev algebra [Formula: see text]. In this paper we explicitly give all MPJ-structures on some interesting classes of Malcev algebras. Further, we introduce the concept of pseudo-Euclidean MPJ-algebras (PEMPJ-algebras) and we show how one can construct new interesting quadratic Lie algebras and pseudo-Euclidean Malcev (non-Lie) algebras from PEMPJ-algebras. Finally, we give inductive descriptions of nilpotent PEMPJ-algebras.

APA, Harvard, Vancouver, ISO, and other styles

2

Kalnins, Ernest G., and W. Miller. "Quadratic algebra contractions and second-order superintegrable systems." Analysis and Applications 12, no. 05 (August 28, 2014): 583–612. http://dx.doi.org/10.1142/s0219530514500377.

Full text

Abstract:

Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of second-order superintegrable systems in two dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. For constant curvature spaces, we show that the free quadratic algebras generated by the first- and second-order elements in the enveloping algebras of their Euclidean and orthogonal symmetry algebras correspond one-to-one with the possible superintegrable systems with potential defined on these spaces. We describe a contraction theory for quadratic algebras and show that for constant curvature superintegrable systems, ordinary Lie algebra contractions induce contractions of the quadratic algebras of the superintegrable systems that correspond to geometrical pointwise limits of the physical systems. One consequence is that by contracting function space realizations of representations of the generic superintegrable quantum system on the 2-sphere (which give the structure equations for Racah/Wilson polynomials) to the other superintegrable systems one obtains the full Askey scheme of orthogonal hypergeometric polynomials.

APA, Harvard, Vancouver, ISO, and other styles

3

BLOHMANN, CHRISTIAN. "PERTURBATIVE SYMMETRIES ON NONCOMMUTATIVE SPACES." International Journal of Modern Physics A 19, no. 32 (December 30, 2004): 5693–706. http://dx.doi.org/10.1142/s0217751x04021238.

Full text

Abstract:

Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semisimple Lie algebras with respect to formal deformations is reviewed in the context of star products. It is shown that rigidity of symmetry algebras extends to rigidity of the action of the symmetry on the space. This implies that the noncommutative spaces considered can be realized as star products by particular ordering prescriptions which are compatible with the symmetry. These symmetry preserving ordering prescriptions are calculated for the quantum plane and four-dimensional quantum Euclidean space. The result can be used to construct invariant Lagrangians for quantum field theory on noncommutative spaces with a deformed symmetry.

APA, Harvard, Vancouver, ISO, and other styles

4

SANTANDER, MARIANO. "A PERSPECTIVE ON THE MAGIC SQUARE AND THE "SPECIAL UNITARY" REALIZATION OF REAL SIMPLE LIE ALGEBRAS." International Journal of Geometric Methods in Modern Physics 10, no. 08 (August 7, 2013): 1360002. http://dx.doi.org/10.1142/s0219887813600025.

Full text

Abstract:

This paper contains the last part of the minicourse "Spaces: A Perspective View" delivered at the IFWGP2012. The series of three lectures was intended to bring the listeners from the more naive and elementary idea of space as "our physical Space" (which after all was the dominant one up to the 1820s) through the generalization of the idea of space which took place in the last third of the 19th century. That was a consequence of first the discovery and acceptance of non-Euclidean geometry and second, of the views afforded by the works of Riemann and Klein and continued since then by many others, outstandingly Lie and Cartan. Here we deal with the part of the minicourse which centers on the classification questions associated to the simple real Lie groups. We review the original introduction of the Magic Square "á la Freudenthal", putting the emphasis in the role played in this construction by the four normed division algebras ℝ, ℂ, ℍ, 𝕆. We then explore the possibility of understanding some simple real Lie algebras as "special unitary" over some algebras 𝕂 or tensor products 𝕂1 ⊗ 𝕂2, and we argue that the proper setting for this construction is not to confine only to normed division algebras, but to allow the split versions ℂ′, ℍ′, 𝕆′ of complex, quaternions and octonions as well. This way we get a "Grand Magic Square" and we fill in all details required to cover all real forms of simple real Lie algebras within this scheme. The paper ends with the complete lists of all realizations of simple real Lie algebras as "special unitary" (or only unitary when n = 2) over some tensor product of two *-algebras 𝕂1, 𝕂2, which in all cases are obtained from ℝ, ℂ, ℂ′, ℍ, ℍ′, 𝕆, 𝕆′ as sets, endowing them with a *-conjugation which usually but not always is the natural complex, quaternionic or octonionic conjugation.

APA, Harvard, Vancouver, ISO, and other styles

5

Izmest'ev, A. A., G. S. Pogosyan, A. N. Sissakian, and P. Winternitz. "Contractions of Lie Algebras and Separation of Variables." International Journal of Modern Physics A 12, no. 01 (January 10, 1997): 53–61. http://dx.doi.org/10.1142/s0217751x97000074.

Full text

Abstract:

The Inönü-Wigner contraction from the Lorentz group O(2,1) to the Euclidean group E(2) is used to relate the separation of variables in the Laplace-Beltrami operators on the two corresponding homogeneous spaces. We consider the contractions on four levels: the Lie algebra, the commuting sets of second order operators in the enveloping algebra o(2,1), the coordinate systems and some eigenfunctions of the Laplace-Beltrami operators.

APA, Harvard, Vancouver, ISO, and other styles

6

ANDERSON, ARLEN. "SYMMETRIC SPACE TWO-MATRIX MODELS." International Journal of Modern Physics A 07, no. 23 (September 20, 1992): 5781–96. http://dx.doi.org/10.1142/s0217751x92002635.

Full text

Abstract:

The radial form of the partition function of a two-matrix model is formally given in terms of a spherical function for matrices representing any Euclidean symmetric space. An explicit expression is obtained by constructing the spherical function by the method of intertwining. The reduction of two-matrix models based on Lie algebras is an elementary application. A model based on the rank one symmetric space isomorphic to RN is less trivial and is treated in detail. This model may be interpreted as an Ising model on a random branched polymer. It has the unusual feature that the maximum order of criticality is different in the planar and double-scaling limits.

APA, Harvard, Vancouver, ISO, and other styles

7

Cortés, V., L. Gall, and T. Mohaupt. "Four-dimensional vector multiplets in arbitrary signature (I)." International Journal of Geometric Methods in Modern Physics 17, no. 10 (August 26, 2020): 2050150. http://dx.doi.org/10.1142/s0219887820501509.

Full text

Abstract:

We derive a necessary and sufficient condition for Poincaré Lie superalgebras in any dimension and signature to be isomorphic. This reduces the classification problem, up to certain discrete operations, to classifying the orbits of the Schur group on the vector space of superbrackets. We then classify four-dimensional [Formula: see text] supersymmetry algebras, which are found to be unique in Euclidean and in neutral signature, while in Lorentz signature there exist two algebras with R-symmetry groups [Formula: see text] and [Formula: see text], respectively.

APA, Harvard, Vancouver, ISO, and other styles

8

DOUGLAS, ANDREW, and JOE REPKA. "INDECOMPOSABLE REPRESENTATIONS OF THE EUCLIDEAN ALGEBRA 𝔢(3) FROM IRREDUCIBLE REPRESENTATIONS OF." Bulletin of the Australian Mathematical Society 83, no. 3 (April 1, 2011): 439–49. http://dx.doi.org/10.1017/s0004972711002115.

Full text

Abstract:

AbstractThe Euclidean group E(3) is the noncompact, semidirect product group E(3)≅ℝ3⋊SO(3). It is the Lie group of orientation-preserving isometries of three-dimensional Euclidean space. The Euclidean algebra 𝔢(3) is the complexification of the Lie algebra of E(3). We embed the Euclidean algebra 𝔢(3) into the simple Lie algebra $\mathfrak {sl}(4,\mathbb {C})$ and show that the irreducible representations V (m,0,0) and V (0,0,m) of $\mathfrak {sl}(4,\mathbb {C})$ are 𝔢(3)-indecomposable, thus creating a new class of indecomposable 𝔢(3) -modules. We then show that V (0,m,0) may decompose.

APA, Harvard, Vancouver, ISO, and other styles

9

POPOV, A. D. "SELF-DUAL YANG–MILLS: SYMMETRIES AND MODULI SPACE." Reviews in Mathematical Physics 11, no. 09 (October 1999): 1091–149. http://dx.doi.org/10.1142/s0129055x99000350.

Full text

Abstract:

Geometry of the solution space of the self-dual Yang–Mills (SDYM) equations in Euclidean four-dimensional space is studied. Combining the twistor and group-theoretic approaches, we describe the full infinite-dimensional symmetry group of the SDYM equations and its action on the space of local solutions to the field equations. It is argued that owing to the relation to a holomorphic analogue of the Chern–Simons theory, the SDYM theory may be as solvable as 2D rational conformal field theories, and successful nonperturbative quantization may be developed. An algebra acting on the space of self-dual conformal structures on a 4-space (an analogue of the Virasoro algebra) and an algebra acting on the space of self-dual connections (an analogue of affine Lie algebras) are described. Relations to problems of topological and N=2 strings are briefly discussed.

APA, Harvard, Vancouver, ISO, and other styles

10

Cortés, V., L. Gall, and T. Mohaupt. "Four-dimensional vector multiplets in arbitrary signature (II)." International Journal of Geometric Methods in Modern Physics 17, no. 10 (August 26, 2020): 2050151. http://dx.doi.org/10.1142/s0219887820501510.

Full text

Abstract:

Following the classification up to isomorphism of [Formula: see text] Poincaré Lie superalgebras in four dimensions with arbitrary signature obtained in a companion paper, we present off-shell vector multiplet representations and invariant Lagrangians realizing these algebras. By dimensional reduction of five-dimensional off-shell vector multiplets, we obtain two representations in each four-dimensional signature. In Euclidean and neutral signature, these representations can be mapped to each other by a field redefinition induced by the action of the Schur group on the space of superbrackets. In Minkowski signature, we show that the superbrackets underlying the two vector multiplet representations belong to distinct open orbits of the Schur group and are therefore inequivalent. Our formalism allows to answer questions about the possible relative signs between terms in the Lagrangian systematically by relating them to the underlying space of superbrackets.

APA, Harvard, Vancouver, ISO, and other styles

More sources

Dissertations / Theses on the topic "Lie algebras][Euclidean space"

1

Gover, Ashwin Roderick. "A geometrical construction of conformally invariant differential operators." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329953.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Wickramasekara, Sujeewa, and sujeewa@physics utexas edu. "Symmetry Representations in the Rigged Hilbert Space Formulation of." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi993.ps.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Günther, Janne-Kathrin. "The C*-algebras of certain Lie groups." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0118/document.

Full text

Abstract:

Dans la présente thèse de doctorat, les C*-algèbres des groupes de Lie connexes réels nilpotents de pas deux et du groupe de Lie SL(2,R) sont caractérisées. En outre, comme préparation à une analyse de sa C*-algèbre, la topologie du spectre du produit semi-direct U(n) x H_n est décrite, où H_n dénote le groupe de Lie de Heisenberg et U(n) le groupe unitaire qui agit sur H_n par automorphismes. Pour la détermination des C*-algèbres de groupes, la transformation de Fourier à valeurs opérationnelles est utilisée pour appliquer chaque C*-algèbre dans l'algèbre de tous les champs d'opérateurs bornés sur son spectre. On doit trouver les conditions que satisfait l'image de cette C*-algèbre sous la transformation de Fourier et l'objectif est de la caractériser par ces conditions. Dans cette thèse, il est démontré que les C*-algèbres des groupes de Lie connexes réels nilpotents de pas deux et la C*-algèbre de SL(2,R) satisfont les mêmes conditions, des conditions appelées «limites duales sous contrôle normique». De cette manière, ces C*-algèbres sont décrites dans ce travail et les conditions «limites duales sous contrôle normique» sont explicitement calculées dans les deux cas. Les méthodes utilisées pour les groupes de Lie nilpotents de pas deux et pour le groupe SL(2,R) sont très différentes l'une de l'autre. Pour les groupes de Lie nilpotents de pas deux, on regarde leurs orbites coadjointes et on utilise la théorie de Kirillov, alors que pour le groupe SL(2,R), on peut mener les calculs plus directement
In this doctoral thesis, the C*-algebras of the connected real two-step nilpotent Lie groups and the Lie group SL(2,R) are characterized. Furthermore, as a preparation for an analysis of its C*-algebra, the topology of the spectrum of the semidirect product U(n) x H_n is described, where H_n denotes the Heisenberg Lie group and U(n) the unitary group acting by automorphisms on H_n. For the determination of the group C*-algebras, the operator valued Fourier transform is used in order to map the respective C*-algebra into the algebra of all bounded operator fields over its spectrum. One has to find the conditions that are satisfied by the image of this C*-algebra under the Fourier transform and the aim is to characterize it through these conditions. In the present thesis, it is proved that both the C*-algebras of the connected real two-step nilpotent Lie groups and the C*-algebra of SL(2,R) fulfill the same conditions, namely the “norm controlled dual limit” conditions. Thereby, these C*-algebras are described in this work and the “norm controlled dual limit” conditions are explicitly computed in both cases. The methods used for the two-step nilpotent Lie groups and the group SL(2,R) are completely different from each other. For the two-step nilpotent Lie groups, one regards their coadjoint orbits and uses the Kirillov theory, while for the group SL(2,R) one can accomplish the calculations more directly

APA, Harvard, Vancouver, ISO, and other styles

4

Nunes, Castanheira da Costa Jose Manuel. "Affine and curvature collineations in space-time." Thesis, University of Aberdeen, 1989. http://digitool.abdn.ac.uk/R?func=search-advanced-go&find_code1=WSN&request1=AAIU602256.

Full text

Abstract:

The purpose of this thesis is the study of the Lie algebras of affine vector fields and curvature collineations of space-time, the aim being, in the first case, to obtain upper bounds on the dimension of the Lie algebra of affine vector fields (under the assumption that the space-time is non-flat) as well as to obtain a characterization of such vector fields in terms of other types of symmetries. In the case of curvature collineations the aim was that of characterizing space-times which may admit an infinite-dimensional Lie algebra of curvature collineations as well as to find local characterizations of such vector fields. Chapters 1 and 2 consist of introductory material, in Differential Geometry (Ch.l) and General Relativity (Ch.2). In Chapter 3 we study homothetic vector fields which admit fixed points. The general results of Alekseevsky (a) and Hall (b) are presented, some being deduced by different methods. Some further details and results are also given. Chapter 4 is concerned with space-times that can admit proper affine vector fields. Using the holonomy classification obtained by Hall (c) it is shown that there are essentially two classes to consider. These classes are analysed in detail and upper bounds on the dimension of the Lie algebra of affine vector fields of such space-times are obtained. In both cases local characterizations of affine vector fields are obtained. Chapter 5 is concerned with space-times which may admit proper curvature collineations. Using the results of Halford and McIntosh (d) , Hall and McIntosh (e) and Hall (f) we were able to divide our study into several classes The last two of these classes are formed by those space-times which admit a (1 or 2-dimensional) non-null distribution spanned by vector fields which contract the Riemann tensor to zero. A complete analysis of each class is made and some general results concerning the infinite-dimensionality problem are proved. The chapter ends with some comments in the cases when the distribution mentioned above is null.

APA, Harvard, Vancouver, ISO, and other styles

5

Rees, Michael K. "Topological uniqueness results for the special linear and other classical Lie Algebras." Thesis, University of North Texas, 2001. https://digital.library.unt.edu/ark:/67531/metadc3000/.

Full text

Abstract:

Suppose L is a complete separable metric topological group (ring, field, etc.). L is topologically unique if the Polish topology on L is uniquely determined by its underlying algebraic structure. More specifically, L is topologically unique if an algebraic isomorphism of L with any other complete separable metric topological group (ring, field, etc.) induces a topological isomorphism. A local field is a locally compact topological field with non-discrete topology. The only local fields (up to isomorphism) are the real, complex, and p-adic numbers, finite extensions of the p-adic numbers, and fields of formal power series over finite fields. We establish the topological uniqueness of the special linear Lie algebras over local fields other than the complex numbers (for which this result is not true) in the context of complete separable metric Lie rings. Along the way the topological uniqueness of all local fields other than the field of complex numbers is established, which is derived as a corollary to more general principles which can be applied to a larger class of topological fields. Lastly, also in the context of complete separable metric Lie rings, the topological uniqueness of the special linear Lie algebra over the real division algebra of quaternions, the special orthogonal Lie algebras, and the special unitary Lie algebras is proved.

APA, Harvard, Vancouver, ISO, and other styles

6

Sawada, Koichiro. "Reconstruction of invariants of configuration spaces of hyperbolic curves from associated Lie algebras." Kyoto University, 2019. http://hdl.handle.net/2433/242578.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Costa, José Manuel Nunes Castanheira da. "Affine and curvature collineations in space-time." Doctoral thesis, University of Aberdeen, 1989. http://hdl.handle.net/10400.13/203.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Lai, Yi-Hong, and 賴奕宏. "Application of the Lie-group scheme on solving nonlinear sloshing problems in Euclidean space." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/55415541454989693830.

Full text

Abstract:

碩士
國立臺灣海洋大學
輪機工程學系
104
Based on the GL(n,R), an equal norm multiple scale Trefftz method (MSTM) associated with Lie-group scheme in Euclidean space is developed to describe nonlinear sloshing behaviors. When the non-linear sloshing phenomena are encountered in Trefftz method, some difficulties, like the boundary conditions with noisy perturbation, ill-conditioned system by using higher-order T-complete functions, controlled volume correction, and characteristic length selection, need to be overcome simultaneously. To tackle these complicated problems, the MSTM combined with the vector regularization method (VRM) is first adopted to eliminate the higher-order numerical oscillation phenomena and noisy dissipation in boundary value problem. Then, the weighting factors of initial- and boundary value problems are introduced into the linear system to prevent the elevation from vanishing without iterative computational controlled volume. More importantly, we combined the explicit scheme based on the GL(n,R) with implicit scheme to reduce iteration number and increase computational efficiency. A comparison of the results of the present study with those in the literature shows that the proposed approach is better than previously reported methods and presents a simple and stable way to cope with the nonlinear sloshing problems.

APA, Harvard, Vancouver, ISO, and other styles

9

Sajedi, Masoumeh. "Classification of separable superintegrable systems of order four in two dimensional Euclidean space and algebras of integrals of motion in one dimension." Thèse, 2019. http://hdl.handle.net/1866/21748.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

Abdul-Reda, Hassan. "Intégrabilité et superintégrabilité de deuxième ordre dans l'espace Euclidien tridimensionel." Thesis, 2020. http://hdl.handle.net/1866/23971.

Full text

Abstract:

L'article "A systematic search for nonrelativistic systems with dynamical symetries, Part I" publié il y a à peu près 50 ans a commencé une classification de ce qui est maintenant appelé les systèmes superintégrables. Il était dévoué aux systèmes dans l'espace Euclidien ayant plus d'intégrales de mouvement que de degrés de liberté. Les intégrales étaient toutes supposées de second ordre en quantité de mouvement. Dans ce mémoire, sont présentés de nouveaux résultats sur la superintégrabilité de second ordre qui sont pertinents à l'étude de la superintégrabilité d'ordre supérieur et de la superintégrabilité de systèmes ayant des potentiels vecteurs ou des particules avec spin.
The article "A systematic search for nonrelativistic systems with dynamical symetries, Part I" published about 50 years ago started the classification of what is now called superintegrable systems. It was devoted to systems in Euclidean space with more integrals of motion than degrees of freedom. The integrals were all assumed to be second order polynomials in the particle momentum. Here we present some further results on second order superintegrability that are relevant for studies of higher order superintegrability and for superintegrability for systems with vector potentials or for particles with spin.

APA, Harvard, Vancouver, ISO, and other styles

Books on the topic "Lie algebras][Euclidean space"

1

Jakobsen, Hans Plesner. The full set of unitarizable highest weight modules of basic classical Lie superalgebras. Providence, RI: American Mathematical Society, 1994.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

2

Christensen, Jens Gerlach. Trends in harmonic analysis and its applications: AMS special session on harmonic analysis and its applications : March 29-30, 2014, University of Maryland, Baltimore County, Baltimore, MD. Providence, Rhode Island: American Mathematical Society, 2015.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

3

1980-, Blazquez-Sanz David, Morales Ruiz, Juan J. (Juan José), 1953-, and Lombardero Jesus Rodriguez 1961-, eds. Symmetries and related topics in differential and difference equations: Jairo Charris Seminar 2009, Escuela de Matematicas, Universidad Sergio Arboleda, Bogotá, Colombia. Providence, R.I: American Mathematical Society, 2011.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

4

Simon, Barry. Operator theory. Providence, Rhode Island: American Mathematical Society, 2015.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

5

J, Sally Paul. Fundamentals of mathematical analysis. Providence, Rhode Island: American Mathematical Society, 2013.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

6

The Moduli Space of N=1 Superspheres With Tubes and the Sewing Operation. American Mathematical Society, 2003.

Find full text

APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Lie algebras][Euclidean space"

1

Zeidler, Eberhard. "The Euclidean Space E 3 (Hilbert Space and Lie Algebra Structure)." In Quantum Field Theory III: Gauge Theory, 69–114. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22421-8_2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

Turbiner, A. "Lie algebras in Fock space." In Complex Analysis and Related Topics, 265–84. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8698-7_18.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

Boudet, Roger. "Real Algebras Associated with an Euclidean Space." In Quantum Mechanics in the Geometry of Space-Time, 105–9. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-19199-2_14.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Nikolov, Nikolay M., Raymond Stora, and Ivan Todorov. "Euclidean Configuration Space Renormalization, Residues and Dilation Anomaly." In Lie Theory and Its Applications in Physics, 127–47. Tokyo: Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54270-4_9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Mickelsson, Jouko. "Current Algebras as Hilbert Space Operator Cocycles." In Noncompact Lie Groups and Some of Their Applications, 373–90. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1078-5_25.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Seligman, George B. "Non-reduced excepticnal algebras with a one-dimensional root space." In Constructions of Lie Algebras and their Modules, 115–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0079302.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Führ, Hartmut. "Continuous Diffusion Wavelet Transforms and Scale Space over Euclidean Spaces and Noncommutative Lie Groups." In Computational Imaging and Vision, 123–36. London: Springer London, 2011. http://dx.doi.org/10.1007/978-1-4471-2353-8_7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Bincer, Adam M. "The Coulomb problem in n space dimensions." In Lie Groups and Lie Algebras, 189–95. Oxford University Press, 2012. http://dx.doi.org/10.1093/acprof:oso/9780199662920.003.0021.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

"Lie Algebras and Lie Groups: Basic Notions." In Linear Ray and Wave Optics in Phase Space, 519–22. Elsevier, 2005. http://dx.doi.org/10.1016/b978-044451799-9/50010-8.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

"Weight Space and Lie’s Lemma and Theorem." In Classical and Quantum Mechanics with Lie Algebras, 485–93. WORLD SCIENTIFIC, 2021. http://dx.doi.org/10.1142/9789811240065_0019.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Lie algebras][Euclidean space"

1

Bru¨ls, Olivier, Martin Arnold, and Alberto Cardona. "Two Lie Group Formulations for Dynamic Multibody Systems With Large Rotations." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48132.

Full text

Abstract:

This paper studies the formulation of the dynamics of multibody systems with large rotation variables and kinematic constraints as differential-algebraic equations on a matrix Lie group. Those equations can then be solved using a Lie group time integration method proposed in a previous work. The general structure of the equations of motion are derived from Hamilton principle in a general and unifying framework. Then, in the case of rigid body dynamics, two particular formulations are developed and compared from the viewpoint of the structure of the equations of motion, of the accuracy of the numerical solution obtained by time integration, and of the computational cost of the iteration matrix involved in the Newton iterations at each time step. In the first formulation, the equations of motion are described on a Lie group defined as the Cartesian product of the group of translations R3 (the Euclidean space) and the group of rotations SO(3) (the special group of 3 by 3 proper orthogonal transformations). In the second formulation, the equations of motion are described on the group of Euclidean transformations SE(3) (the group of 4 by 4 homogeneous transformations). Both formulations lead to a second-order accurate numerical solution. For an academic example, we show that the formulation on SE(3) offers the advantage of an almost constant iteration matrix.

APA, Harvard, Vancouver, ISO, and other styles

2

Valderrama-Rodríguez, Juan Ignacio, José M. Rico, J. Jesús Cervantes-Sánchez, and Fernando Tomás Pérez-Zamudio. "A New Look to the Three Axes Theorem." In ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/detc2019-97443.

Full text

Abstract:

Abstract This paper analyzes the well known three axes theorem under the light of the Lie algebra se(3) of the Euclidean group, SE(3) and the symmetric bilinear forms that can be defined in this algebra. After a brief historical review of the Aronhold-Kennedy theorem and its spatial generalization, the main hypothesis is that the general version of the Aronhold-Kennedy theorem is basically the application of the Killing and Klein forms to the equation that relates the velocity states of three bodies regardless if they are free to move in the space, independent of each other, or they form part of a kinematic chain. Two representative examples are employed to illustrate the hypothesis, one where the rigid bodies are free to move in the space without any connections among them and other concerning a RCCC spatial mechanism.

APA, Harvard, Vancouver, ISO, and other styles

3

FIALOWSKI, ALICE. "THE MODULI SPACE AND VERSAL DEFORMATIONS OF THREE DIMENSIONAL LIE ALGEBRAS." In Proceedings of the International Conference on Algebras, Modules and Rings. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774552_0008.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Kime, Katherine A. "Control Lie Algebras of Semi-Discretizations of the Schroedinger Equation." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35105.

Full text

Abstract:

We consider control of the one-dimensional Schroedinger equation via a time-dependent rectangular potential. We discretize the equation in the space variable, obtaining a system of ODEs in which the control is bilinear. We find Control Lie Algebras for several cases, including single point and full width potentials. We use full discretizations, in space and time, to examine the effect of the number of inputs.

APA, Harvard, Vancouver, ISO, and other styles

5

Kime, Katherine A. "Effect of the Spatial Extent of the Control in a Bilinear Control Problem for the Schroedinger Equation." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86440.

Full text

Abstract:

We consider control of the one-dimensional Schroedinger equation through a time-varying potential. Using a finite difference semi-discretization, we consider increasing the extent of the potential from a single central grid-point in space to two or more gridpoints. With the differential geometry package in Maple 8, we compute and compare the corresponding Control Lie Algebras, identifying a trend in the number of elements which span the Control Lie Algebras.

APA, Harvard, Vancouver, ISO, and other styles

6

Izadi, Maziar, Jan Bohn, Daero Lee, Amit K. Sanyal, Eric Butcher, and Daniel J. Scheeres. "A Nonlinear Observer Design for a Rigid Body in the Proximity of a Spherical Asteroid." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-4085.

Full text

Abstract:

We consider an observer design for a spacecraft modeled as a rigid body in the proximity of an asteroid. The nonlinear observer is constructed on the nonlinear state space of motion of a rigid body, which is the tangent bundle of the Lie group of rigid body motions in three-dimensional Euclidean space. The framework of geometric mechanics is used for the observer design. States of motion of the spacecraft are estimated based on state measurements. In addition, the observer designed can also estimate the gravity parameter of the asteroid, assuming the asteroid to have a spherically symmetric mass distribution. Almost global convergence of state estimates and gravity parameter estimate to their corresponding true values is demonstrated analytically, and verified numerically.

APA, Harvard, Vancouver, ISO, and other styles

7

Chu, Y. X., J. B. Gou, and Z. X. Li. "A Geometric Algorithm for Hybrid Workpiece Localization/Envelopment Problem." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/dfm-5745.

Full text

Abstract:

Abstract The problem of aligning the CAD model of a workpiece such that all points measured on the finished surfaces of the workpiece match closely to corresponding surfaces on the model while all unmachined surfaces lie outside the model to guarantee the presence of material to be machined at a later time is referred to as the hybrid localization/envelopment problem. The hybrid problem has important applications in setting up for machining of partially finished workpieces. This paper gives a formulation of the hybrid localization/envelopment problem and present a geometric algorithm for computing its solutions. First, we show that when the finished surfaces of a workpiece are inadequate to fully constrain the rigid motions of the workpiece, then the set of free motions remaining must form a subgroup G0 of the Euclidean group SE(3). This allows us to decompose the hybrid problem into a (symmetric) localization problem on the homogeneous space SE(3)/G0 and an envelopment problem on G0. While the symmetric localization problem is solved using the Fast Symmetric Localization (FSL) algorithm developed in one of our early papers, the envelopment problem is solved by computing the solutions of a sequence of linear programming (LP) problems. We derive explicitly the LP problems and apply standard linear programming techniques to solve the LP problems. We present simulation results to demonstrate efficiency of our method for the hybrid problem.

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!