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Relevant bibliographies by topics / Group algebras; Symmetry

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Academic literature on the topic 'Group algebras; Symmetry'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Group algebras; Symmetry"

1

Skalski, Adam, and Piotr M. Sołtan. "Projective limits of quantum symmetry groups and the doubling construction for Hopf algebras." Infinite Dimensional Analysis, Quantum Probability and Related Topics 17, no. 02 (May 28, 2014): 1450012. http://dx.doi.org/10.1142/s021902571450012x.

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The quantum symmetry group of the inductive limit of C*-algebras equipped with orthogonal filtrations is shown to be the projective limit of the quantum symmetry groups of the C*-algebras appearing in the sequence. Some explicit examples of such projective limits are studied, including the case of quantum symmetry groups of the duals of finite symmetric groups, which do not fit directly into the framework of the main theorem and require further specific study. The investigations reveal a deep connection between quantum symmetry groups of discrete group duals and the doubling construction for Hopf algebras.

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Rong, Shu-Jun. "New Partial Symmetries from Group Algebras for Lepton Mixing." Advances in High Energy Physics 2020 (February 8, 2020): 1–8. http://dx.doi.org/10.1155/2020/3967605.

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Recent stringent experiment data of neutrino oscillations induces partial symmetries such as Z2 and Z2×CP to derive lepton mixing patterns. New partial symmetries expressed with elements of group algebras are studied. A specific lepton mixing pattern could correspond to a set of equivalent elements of a group algebra. The transformation which interchanges the elements could express a residual CP symmetry. Lepton mixing matrices from S3 group algebras are of the trimaximal form with the μ−τ reflection symmetry. Accordingly, elements of S3 group algebras are equivalent to Z2×CP. Comments on S4 group algebras are given. The predictions of Z2×CP broken from the group S4 with the generalized CP symmetry are also obtained from elements of S4 group algebras.

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Walker, Martin. "SU(2) × SU(2) Algebras and the Lorentz Group O(3,3)." Symmetry 12, no. 5 (May 15, 2020): 817. http://dx.doi.org/10.3390/sym12050817.

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The Lie algebra of the Lorentz group O(3,3) admits two types of SU(2) × SU(2) subalgebras: a standard form based on spatial rotation generators and a second form based on temporal rotation generators. The units of measurement for the conserved quantity due to invariance under temporal rotations are investigated and found to be the same units of measure as the Planck constant. The breaking of time reversal symmetry is considered and found to affect the chiral properties of a temporal SU(2) × SU(2) algebra. Finally, the symmetry between algebras is explored and pairs of algebras are found to be related by SU(2) × U(1) symmetry, while a group of three algebras are related by SO(4) symmetry.

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KERNER, RICHARD, and OSAMU SUZUKI. "INTERNAL SYMMETRY GROUPS OF CUBIC ALGEBRAS." International Journal of Geometric Methods in Modern Physics 09, no. 06 (August 3, 2012): 1261007. http://dx.doi.org/10.1142/s0219887812610075.

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We investigate certain Z3-graded associative algebras with cubic Z3 invariant constitutive relations, introduced by one of us some time ago. The invariant forms on finite algebras of this type are given in the cases with two and three generators. We show how the Lorentz symmetry represented by the SL (2, C) group can be introduced without any notion of metric, just as the symmetry of Z3-graded cubic algebra and its constitutive relations. Its representation is found in terms of the Pauli matrices. The relationship of such algebraic constructions with quark states is also considered.

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Green, HS. "A Cyclic Symmetry Principle in Physics." Australian Journal of Physics 47, no. 1 (1994): 25. http://dx.doi.org/10.1071/ph940025.

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Many areas of modern physics are illuminated by the application of a symmetry principle, requiring the invariance of the relevant laws of physics under a group of transformations. This paper examines the implications and some of the applications of the principle of cyclic symmetry, especially in the areas of statistical mechanics and quantum mechanics, including quantized field theory. This principle requires invariance under the transformations of a finite group, which may be a Sylow 7r-group, a group of Lie type, or a symmetric group. The utility of the principle of cyclic invariance is demonstrated in finding solutions of the Yang-Baxter equation that include and generalize known solutions. It is shown that the Sylow 7r-groups have other uses, in providing a basis for a type of generalized quantum statistics, and in parametrising a new generalization of Lie groups, with associated algebras that include quantized algebras.

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ĐAPIĆ, N., M. KUNZINGER, and S. PILIPOVIĆ. "SYMMETRY GROUP ANALYSIS OF WEAK SOLUTIONS." Proceedings of the London Mathematical Society 84, no. 3 (April 29, 2002): 686–710. http://dx.doi.org/10.1112/s0024611502013436.

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Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and non-linear) partial differential equations, where the term `weak solution' comprises the following settings: distributional solutions; solutions in generalized function algebras; solutions in the sense of association (corresponding to a number of weak or integral solution concepts in classical analysis). Factorization properties and infinitesimal criteria that allow the treatment of all three settings simultaneously are developed, thereby unifying and extending previous work in this area.2000 Mathematical Subject Classification: 46F30, 22E70, 35Dxx, 35A30.

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Elduque, Alberto, and Susumu Okubo. "Special Freudenthal–Kantor triple systems and Lie algebras with dicyclic symmetry." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 141, no. 6 (November 15, 2011): 1225–62. http://dx.doi.org/10.1017/s0308210510000569.

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We study Lie algebras endowed with an action by automorphisms of the dicyclic group of degree 3. The close connections of these algebras with Lie algebras graded over the non-reduced root system BC1, with J-ternary algebras and with Freudenthal–Kantor triple systems are explored.

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Joardar, Soumalya, and Arnab Mandal. "Quantum symmetry of graph C∗-algebras associated with connected graphs." Infinite Dimensional Analysis, Quantum Probability and Related Topics 21, no. 03 (September 2018): 1850019. http://dx.doi.org/10.1142/s0219025718500194.

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We define a notion of quantum automorphism groups of graph [Formula: see text]-algebras for finite, connected graphs. Under the assumption that the underlying graph does not have any multiple edge or loop, the quantum automorphism group of the underlying directed graph in the sense of Banica [Quantum automorphism groups of homogeneous graphs, J. Funct. Anal. 224 (2005) 243–280] (which is also the symmetry object in the sense of [S. Schmidt and M. Weber, Quantum symmetry of graph [Formula: see text]-algebras, arXiv:1706.08833 ] is shown to be a quantum subgroup of quantum automorphism group in our sense. Quantum symmetries for some concrete graph [Formula: see text]-algebras have been computed.

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Kamiya, Noriaki, and Susumu Okubo. "Symmetry of Lie algebras associated with (ε, δ)-Freudenthal-Kantor triple system." Proceedings of the Edinburgh Mathematical Society 59, no. 1 (July 13, 2015): 169–92. http://dx.doi.org/10.1017/s0013091514000406.

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AbstractSymmetry groups of Lie algebras and superalgebras constructed from (∈, δ)-Freudenthal-Kantor triple systems have been studied. In particular, for a special (ε, ε)-Freudenthal–Kantor triple, it is the SL(2) group. Also, the relationship between two constructions of Lie algebras from structurable algebras has been investigated.

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DOLAN, L., and M. LANGHAM. "SYMMETRIC SUBGROUPS OF GAUGED SUPERGRAVITIES AND AdS STRING THEORY VERTEX OPERATORS." Modern Physics Letters A 14, no. 07 (March 7, 1999): 517–25. http://dx.doi.org/10.1142/s0217732399000572.

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We show how the gauge symmetry representations of the massless particle content of gauged supergravities that arise in the AdS/CFT correspondences can be derived from symmetric subgroups to be carried by string theory vertex operators, although explicit vertex operator constructions of the IIB string on AdS remain elusive. Our symmetry mechanism parallels the construction of representations of the Monster group and affine algebras in terms of twisted conformal field theories, and may serve as a guide to a perturbative description of the IIB string on AdS.

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Dissertations / Theses on the topic "Group algebras; Symmetry"

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Hills, Robert K. "The algebra of a class of permutation invariant irreducible operators." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.260729.

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Moreira, Rodriguez Rivera Walter. "Products of representations of the symmetric group and non-commutative versions." Texas A&M University, 2008. http://hdl.handle.net/1969.1/85938.

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We construct a new operation among representations of the symmetric group that interpolates between the classical internal and external products, which are defined in terms of tensor product and induction of representations. Following Malvenuto and Reutenauer, we pass from symmetric functions to non-commutative symmetric functions and from there to the algebra of permutations in order to relate the internal and external products to the composition and convolution of linear endomorphisms of the tensor algebra. The new product we construct corresponds to the Heisenberg product of endomorphisms of the tensor algebra. For symmetric functions, the Heisenberg product is given by a construction which combines induction and restriction of representations. For non-commutative symmetric functions, the structure constants of the Heisenberg product are given by an explicit combinatorial rule which extends a well-known result of Garsia, Remmel, Reutenauer, and Solomon for the descent algebra. We describe the dual operation among quasi-symmetric functions in terms of alphabets.

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Hill, David Edward. "The Jantzen-Shapovalov form and Cartan invariants of symmetric groups and Hecke algebras /." view abstract or download file of text, 2007. http://proquest.umi.com/pqdweb?did=1400959351&sid=1&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2007.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 107-108). Also available for download via the World Wide Web; free to University of Oregon users.

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Han, Gang. "Clifford algebras associated with symmetric pairs /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20HAN.

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Tan, Kai Meng. "Small defect blocks of symmetric group algebras." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624153.

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Ruff, Oliver. "Completely splittable representations of symmetric groups and affine Hecke algebras /." view abstract or download file of text, 2005. http://wwwlib.umi.com/cr/uoregon/fullcit?p3190545.

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Thesis (Ph. D.)--University of Oregon, 2005.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 44-45). Also available for download via the World Wide Web; free to University of Oregon users.

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Fayers, Matthew. "Representations of symmetric groups and Schur algebras." Thesis, University of Cambridge, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.620642.

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Abubakar, Ahmed Bello. "The structure of symmetric group algebras at arbitrary characteristic." Thesis, University of East London, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.300326.

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Zwicknagl, Sebastian. "Equivariant Poisson algebras and their deformations /." view abstract or download file of text, 2006. http://proquest.umi.com/pqdweb?did=1280144671&sid=2&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Thesis (Ph. D.)--University of Oregon, 2006.
Typescript. Includes vita and abstract. "In this dissertation I investigate Poisson structures on symmetric and exterior algebras of modules over complex reductive Lie algebras. I use the results to study the braided symmetric and exterior algebras"--P. 1. Includes bibliographical references (leaves 150-152). Also available for download via the World Wide Web; free to University of Oregon users.

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Manriquez, Adam. "Symmetric Presentations, Representations, and Related Topics." CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/711.

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The purpose of this thesis is to develop original symmetric presentations of finite non-abelian simple groups, particularly the sporadic simple groups. We have found original symmetric presentations for the Janko group J1, the Mathieu group M12, the Symplectic groups S(3,4) and S(4,5), a Lie type group Suz(8), and the automorphism group of the Unitary group U(3,5) as homomorphic images of the progenitors 2*60 : (2 x A5), 2*60 : A5, 2*56 : (23 : 7), and 2*28 : (PGL(2,7):2), respectively. We have also discovered the groups 24 : A5, 34 : S5, PSL(2,31), PSL(2,11), PSL(2,19), PSL(2,41), A8, 34 : S5, A52, 2• A52, 2 : A62, PSL(2,49), 28 : A5, PGL(2,19), PSL(2,71), 24 : A5, 24 : A6, PSL(2,7), 3 x PSL(3,4), 2• PSL(3,4), PSL(3,4), 2• (M12 : 2), 37:S7, 35 : S5, S6, 25 : S6, 35 : S6, 25 : S5, 24 : S6, and M12 as homomorphic images of the permutation progenitors 2*60 : (2 x A5), 2*60 : A5, 2*21 : (7: 3), 2*60 : (2 x A5), 2*120 : S5, and 2*144 : (32 : 24). We have given original proof of the 2*n Symmetric Presentation Theorem. In addition, we have also provided original proof for the Extension of the Factoring Lemma (involutory and non-involutory progenitors). We have constructed S5, PSL(2,7), and U(3,5):2 using the technique of double coset enumeration and by way of linear fractional mappings. Furthermore, we have given proofs of isomorphism types for 7 x 22, U(3,5):2, 2•(M12 : 2), and (4 x 2) :• 22.

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Books on the topic "Group algebras; Symmetry"

1

A, Lohe M., ed. Quantum group symmetry and q-tensor algebras. Singapore: World Scientific, 1995.

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Iwahori-Hecke algebras and Schur algebras of the symmetric group. Providence, R.I: American Mathematical Society, 1999.

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3

Linear and projective representations of symmetric groups. Cambridge, U.K: Cambridge University Press, 2005.

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4

Symmetric and G-algebras: With applications to group representations. Dordrecht: Kluwer Academic Publishers, 1990.

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5

R, Wallach Nolan, ed. Symmetry, representations, and invariants. Dordrecht [Netherlands]: Springer, 2009.

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Symmetries. [London]: Springer, 2001.

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Fabio, Scarabotti, and Tolli Filippo 1968-, eds. Representation theory of the symmetric groups: The Okounkov-Vershik approach, character formulas, and partition algebras. New York: Cambridge University Press, 2010.

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8

Kerber, Adalbert. Algebraic combinatorics via finite group actions. Mannheim: B.I. Wissenschaftsverlag, 1991.

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9

Evans, David E. Quantum symmetries on operator algebras. Oxford: Clarendon Press, 1998.

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Bernhard, Leeb, and Millson John J. 1946-, eds. The generalized triangle inequalities in symmetric spaces and buildings with applications to algebra. Providence, R.I: American Mathematical Society, 2008.

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Book chapters on the topic "Group algebras; Symmetry"

1

Bump, Daniel. "Some Symmetric Algebras." In Lie Groups, 370–74. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4757-4094-3_46.

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Bump, Daniel. "Some Symmetric Algebras." In Lie Groups, 455–60. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8024-2_44.

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Bonnafé, Cédric. "The Symmetric Group." In Algebra and Applications, 263–71. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-70736-5_22.

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Gallier, Jean, and Jocelyn Quaintance. "Tensor Algebras and Symmetric Algebras." In Differential Geometry and Lie Groups, 11–76. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-46047-1_2.

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Trofimov, V. V. "Lie Groups and Lie Algebras." In Introduction to Geometry of Manifolds with Symmetry, 81–162. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-017-1961-2_2.

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Whitelaw, Thomas A. "The Symmetric Group Sn." In Introduction to Abstract Algebra, 124–51. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4615-7284-8_9.

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Lee, Gregory T. "Symmetric and Alternating Groups." In Abstract Algebra, 101–13. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77649-1_6.

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Gorodentsev, Alexey L. "Representations of Symmetric Groups." In Algebra II, 151–71. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-50853-5_7.

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Shtern, A. I. "Almost Representations and Quasi-Symmetry." In Lie Groups and Lie Algebras, 337–58. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5258-7_21.

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Sehgal, Sudarshan K. "Symmetric Elements and Identities in Group Algebras." In Algebra, 207–13. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-9996-3_13.

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Conference papers on the topic "Group algebras; Symmetry"

1

Yan, Yanxiong, and Guiyun Chen. "OD-Characterization of Alternating and Symmetric Groups of Degree 106 and 112." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0055.

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Venkatesan, R., E. Nandakumar, and Gaverchand K. "Cellularity of signed symmetric group algebras." In 1ST INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2020. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0025270.

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Darafsheh, M. R. "Simple groups which are product of the linear fractional group with the alternating or the symmetric group." In Proceedings of the ICM Satellite Conference in Algebra and Related Topics. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705808_0024.

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Bach, Eric, and Bryce Sandlund. "Baby-Step Giant-Step Algorithms for the Symmetric Group." In ISSAC '16: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2016. http://dx.doi.org/10.1145/2930889.2930930.

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Wybourne, B. G., and M. Yang. "q—Deformation of symmetric functions and Hecke algebras Hn(q) of type An−1." In Group Theory in Physics: Proceedings of the international symposium held in honor of Professor Marcos Moshinsky. AIP, 1992. http://dx.doi.org/10.1063/1.42845.

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Clausen, Michael, and Paul Hühne. "Linear Time Fourier Transforms of S n-k -invariant Functions on the Symmetric Group S n." In ISSAC '17: International Symposium on Symbolic and Algebraic Computation. New York, NY, USA: ACM, 2017. http://dx.doi.org/10.1145/3087604.3087628.

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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.

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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.

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Saghafi, Mehdi, and Harry Dankowicz. "Nondegenerate Continuation Problems for the Excitation Response of Nonlinear Beam Structures." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13115.

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This paper investigates the dynamics of a slender beam subjected to transverse periodic excitation. Of particular interest is the formulation of nondegenerate continuation problems that may be analyzed numerically, in order to explore the parameter-dependence of the steady-state excitation response, while accounting for geometric nonlinearities. Several candidate formulations are presented, including finite-difference (FD) and finite-element (FE) discretizations of the governing scalar, integro-partial differential boundary-value problem (BVP), as well as of a corresponding first-order-in-space, mixed formulation. As an example, a periodic BVP — obtained from a Galerkin-type, FE discretization with continuously differentiable, piecewise-polynomial trial and test functions, and an elimination of Lagrange multipliers associated with spatial boundary conditions — is analyzed to determine the beam response via numerical continuation using a MATLAB-based software suite. In the case of an FE discretization of the mixed formulation with continuous, piecewise-polynomial trial and test functions, it is shown that the choice of spatial boundary conditions may render the resultant index-1, differential-algebraic BVP equivariant under a symmetry group of state-space translations. The paper demonstrates several methods for breaking the equivariance in order to obtain a nondegenerate continuation problem, including a projection onto a symmetry-reduced state space or the introduction of an artificial continuation parameter. As is further demonstrated, an orthogonal collocation discretization in time of the BVP gives rise to ghost solutions, corresponding to arbitrary drift in the algebraic variables. This singularity is resolved by using an asymmetric discretization in time.

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