Relevant bibliographies by topics / Exterior algebra

Academic literature on the topic 'Exterior algebra'

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Published: 4 June 2021
Last updated: 28 January 2023

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Journal articles on the topic "Exterior algebra"

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Marchuk, N. "Generalized Exterior Algebras." Ukrainian Journal of Physics 57, no. 4 (April 30, 2012): 422. http://dx.doi.org/10.15407/ujpe57.4.422.

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Exterior algebras and differential forms are widely used in many fields of modern mathematics and theoretical physics. In this work, we define a notion of N-metric exterior algebra, which depends on N matrices of structure constants. The usual exterior algebra (Grassmann algebra) can be considered as a 0-metric exterior algebra. The Clifford algebra can be considered as a 1-metric exterior algebra. N-metric exterior algebras for N ≥ 2 can be considered as generalizations of the Grassmann and Clifford algebras. Specialists consider models of gravity that are based on a mathematical formalism with two metric tensors. We hope that the 2-metric exterior algebra considered in this work can be useful for the development of this model in gravitation theory and,especially, in the description of fermions in the presence of a gravity field.
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Karaçuha, Serkan, and Christian Lomp. "Integral calculus on quantum exterior algebras." International Journal of Geometric Methods in Modern Physics 11, no. 04 (April 2014): 1450026. http://dx.doi.org/10.1142/s0219887814500261.

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Hom-connections and associated integral forms have been introduced and studied by Brzeziński as an adjoint version of the usual notion of a connection in non-commutative geometry. Given a flat hom-connection on a differential calculus (Ω, d) over an algebra A yields the integral complex which for various algebras has been shown to be isomorphic to the non-commutative de Rham complex (in the sense of Brzeziński et al. [Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom.4 (2010) 281–312]). In this paper we shed further light on the question when the integral and the de Rham complex are isomorphic for an algebra A with a flat Hom-connection. We specialize our study to the case where an n-dimensional differential calculus can be constructed on a quantum exterior algebra over an A-bimodule. Criteria are given for free bimodules with diagonal or upper-triangular bimodule structure. Our results are illustrated for a differential calculus on a multivariate quantum polynomial algebra and for a differential calculus on Manin's quantum n-space.
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Xu, YunGe, Chao Zhang, XiaoJing Ma, and QingFeng Hu. "Hochschild cohomology of Beilinson algebra of exterior algebra." Science China Mathematics 55, no. 6 (May 30, 2012): 1153–70. http://dx.doi.org/10.1007/s11425-012-4388-9.

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Hawrylycz, M. "Dimension independence in exterior algebra." Proceedings of the National Academy of Sciences 92, no. 6 (March 14, 1995): 2323–27. http://dx.doi.org/10.1073/pnas.92.6.2323.

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Johari, Farangis, and Peyman Niroomand. "Certain functors of nilpotent Lie algebras with the derived subalgebra of dimension two." Journal of Algebra and Its Applications 19, no. 01 (March 8, 2019): 2050012. http://dx.doi.org/10.1142/s0219498820500127.

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By considering the nilpotent Lie algebra with the derived subalgebra of dimension [Formula: see text], we compute some functors including the Schur multiplier, the exterior square and the tensor square of these Lie algebras. We also give the corank of such Lie algebras.
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Ali, Md Showkat, K. M. Ahmed, M. R. Khan, and Md Mirazul Islam. "Exterior Algebra with Differential Forms on Manifolds." Dhaka University Journal of Science 60, no. 2 (August 3, 2012): 247–52. http://dx.doi.org/10.3329/dujs.v60i2.11528.

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The concept of an exterior algebra was originally introduced by H. Grassman for the purpose of studying linear spaces. Subsequently Elie Cartan developed the theory of exterior differentiation and successfully applied it to the study of differential geometry [8], [9] or differential equations. More recently, exterior algebra has become powerful and irreplaceable tools in the study of differential manifolds with differential forms and we develop theorems on exterior algebra with examples.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11528 Dhaka Univ. J. Sci. 60(2): 247-252, 2012 (July)
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Kehagias, A. A. "Cuntz deformations of the exterior algebra." Journal of Physics A: Mathematical and General 26, no. 19 (October 7, 1993): L1037—L1046. http://dx.doi.org/10.1088/0305-4470/26/19/011.

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PIKHURKO, OLEG. "Weakly Saturated Hypergraphs and Exterior Algebra." Combinatorics, Probability and Computing 10, no. 5 (September 2001): 435–51. http://dx.doi.org/10.1017/s0963548301004746.

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Given an r-graph F, an r-graph G is called weakly F-saturated if the edges missing from G can be added, one at a time, in some order, each extra edge creating a new copy of F. Let w-sat(n, F) be the minimal size of a weakly F-saturated graph of order n. We compute the w-sat function for a wide class of r-graphs called pyramids: these include many examples for which the w-sat function was known, as well as many new examples, such as the computation of w-sat(n,Ks + Kt), and enable us to prove a conjecture of Tuza.Our main technique, developed from ideas of Kalai, is based on matroids derived from exterior algebra. We prove that if it succeeds for some graphs then the same is true for the ‘cones’ and ‘joins’ of such graphs, so that the w-sat function can be computed for many graphs that are built up from certain elementary graphs by these operations.
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Filliman, P. "Exterior algebra and projections of polytopes." Discrete & Computational Geometry 5, no. 3 (June 1990): 305–22. http://dx.doi.org/10.1007/bf02187792.

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Ramasinghe, W. "Exterior algebra of a Banach space." Bulletin des Sciences Mathématiques 131, no. 3 (April 2007): 291–324. http://dx.doi.org/10.1016/j.bulsci.2006.05.007.

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Dissertations / Theses on the topic "Exterior algebra"

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Shannon, Alexander David John. "Quantum symmetric and exterior algebras." Thesis, University of Cambridge, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.648247.

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Lackey, Joshua. "Properties of ideals in the exterior algebra /." view abstract or download file of text, 2000. http://wwwlib.umi.com/cr/uoregon/fullcit?p9977908.

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Thesis (Ph. D.)--University of Oregon, 2000.
Typescript. Includes vita and abstract. Includes bibliographical references (leaves 92-93). Also available for download via the World Wide Web; free to University of Oregon users.
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Laios, B. A. "A unified approach to decentralised control, based on the exterior algebra and algebraic geometry methods." Thesis, City University London, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.292320.

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Wimelaratna, Ramasinghege. "Multi dimensional geometric moduli and exterior algebra of a Banach space /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu148759830383865.

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Van, Grinsven Jacob. "Generalizations of Discriminants." Bowling Green State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1615805185856192.

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Schüler, Axel. "Äußere Algebren, de-Rham-Kohomologie und Hodge-Zerlegung für Quantengruppen." Doctoral thesis, Universitätsbibliothek Leipzig, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-218057.

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In dieser Arbeit wird die de-Rham-Kohomologie für die Quantengruppen zu den vier klassischen Serien von Lie-Gruppen bestimmt und es wird der Hodgeschen Zerlegungssatz gezeigt. Als entscheidendes Mittel wurde der Laplace-Beltrami-Operator L für Woronowicz’ äußere Algebren entwickelt. Für transzendente Werte von q und reguläre Kalkülparameter z ist L diagonalisierbar. Für die obigen Quantengruppen bestimmen wir die Eigenwerte von L, die neben q und z von zwei integralen dominanten Gewichten abhängen. Wie im klassischen Fall wird die de-Rham-Kohomologie durch harmonische Formen repräsentiert. Jedoch entspricht nur im Fall der A-Serie jeder harmonischen Form auch eine de-Rham-Kohomologieklasse. Im Falle der B-, C- und D-Serien sind biinvariante Formen nicht notwendig geschlossen. Es gilt aber, dass jede biinvariante Form harmonisch ist. Das zweite Hauptresultat ist die Hodge-Zerlegung für die Quantengruppen GLq(N) und SLq(N): Ist der Kalkülparameter z regulär, so lässt sich jede Form eindeutig zerlegen in die Summe aus einem Rand, einem Korand und einem Kohomologierepräsentanten. Ferner gilt, analog zum klassischen Fall, dass die folgenden drei Formenräume übereinstimmen: die biinvarianten Formen, die harmonischen Formen und die de-Rham-Kohomologie. Für die orthogonalen und symplektischen Quantengruppen gibt es keine vollständige Hodge-Zerlegung. Nur für die Elemente, die im Bild des Laplace-Beltrami-Operators liegen, gibt es eine eindeutige Zerlegung in Rand und Korand. Für die Standardkalküle auf den Quantengruppen GLq(N) und SLq(N) wird die Größe von Woronowicz’ äußerer Algebra bestimmt. Es wird gezeigt, dass der Raum der linksinvarianten k-Formen (N² über k)-dimensional ist. Die Algebra der biinvarianten Formen ist graduiert kommutativ. Ihre Poincaré-Reihe ist (1+t)(1+t³) ... (1+t^(2N-1)). Biinvariante Formen sind geschlossen
Consider one of the standard bicovariant first order differential calculi for the quantum groups GLq(N), SLq(N), SOq(N), or SPq(N), where q is a transcendental complex number. It is shown that the de Rham cohomology of Woronowicz' external algebra coincides with the de Rham cohomologies of its left-invariant, its right-invariant and its bi-invariant subcomplexes. In the cases GLq(N) and SLq(N), the cohomology ring is isomorphic to the left-invariant external algebra and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in these cases. The main technical tool is the spectral decomposition of the quantum Laplace-Beltrami operator. As in the classical case all three spaces of differential forms coincide: bi- invariant forms, harmonic forms and the de-Rham-cohomology. For orthog- onal and symplectic quantum groups there is no complete Hodge decompo- sition. In case of the standard calculi on the quantum groups GLq(N) and SLq(N), the size of exterior algebra is computed. The space of left-invariant k-forms has dimension C(N², k) (binomial coefficient). The algebra of bi-invariant forms is graded commutative with Poincaré series (1+t)(1+t³) ... (1+t^(2N-1)). Bi-invariant forms are closed
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Silva, José Naéliton Marques da. "Sobre o Complexo de Koszul." Universidade Federal da Paraí­ba, 2010. http://tede.biblioteca.ufpb.br:8080/handle/tede/7435.

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Made available in DSpace on 2015-05-15T11:46:19Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1046176 bytes, checksum: b07998b12889ca7bedcf163b7e83cd18 (MD5) Previous issue date: 2010-12-20
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
O complexo de Koszul é uma ferramenta de vital importância na Álgebra Comutativa. Ele nos permitirá definir alguns invariantes que nos dão informações refinadas acerca de um determinado módulo. Entre eles podemos ressaltar a profundidade e a multiplicidade de tal módulo em relação à um ideal. A primeira mede o comprimento da maior M-sequência formada por elementos do anel e a segunda nos dà informações assintóticas acerca do comprimento de módulos quocientes
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Olofsson, Rikard. "Supersymmetric Quantum Mechanics and the Gauss-Bonnet Theorem." Thesis, Uppsala universitet, Teoretisk fysik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-355985.

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We introduce the formalism of supersymmetric quantum mechanics, including super-symmetry charges,Z2-graded Hilbert spaces, the chirality operator and the Wittenindex. We show that there is a one to one correspondence of fermions and bosons forenergies different than zero, which implies that the Witten index measures the dif-ference of fermions and bosons at the ground state. We argue that the Witten indexis the index of an elliptic operator. Quantization of the supersymmetric non-linearsigma model shows that the Witten index equals the Euler characteristic of the un-derlying Riemannian manifold over which the theory is defined. Finally, the pathintegral representation of the Witten index is applied to derive the Gauss-Bonnettheorem. Apart from this we introduce elementary mathematical background in thesubjects of topological invariance, Riemannian manifolds and index theory
Vi introducucerar formalismen f ̈or supersymmetrisk kvantmekanik, d ̈aribland super-symmetryladdningar,Z2-graderade Hilbertrum, kiralitetsoperatorn och Wittenin-dexet. Vi visar att det r ̊ader en till en-korrespondens mellan fermioner och bosonervid energiniv ̊aer skillda fr ̊an noll, vilket medf ̈or att Wittenindexet m ̈ater skillnadeni antal fermioner och bosoner vid nolltillst ̊andet. Vi argumenterar f ̈or att Wittenin-dexet ̈ar indexet p ̊a en elliptisk operator. Kvantisering av den supersymmetriskaicke-linj ̈ara sigmamodellen visar att Wittenindexet ̈ar Eulerkarakteristiken f ̈or denunderliggande Riemannska m ̊angfald ̈over vilken teorin ̈ar definierad. Slutligenapplicerar vi v ̈agintegralrepresentationen av Wittenindexet f ̈or att h ̈arleda Gauss-Bonnets sats. Ut ̈over detta introduceras ocks ̊a grundl ̈aggande matematisk bakrundi ämnena topologisk invarians, Riemmanska m ̊angfalder och indexteori.
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Axelsson, Andreas, and kax74@yahoo se. "Transmission problems for Dirac's and Maxwell's equations with Lipschitz interfaces." The Australian National University. School of Mathematical Sciences, 2002. http://thesis.anu.edu.au./public/adt-ANU20050106.093019.

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The aim of this thesis is to give a mathematical framework for scattering of electromagnetic waves by rough surfaces. We prove that the Maxwell transmission problem with a weakly Lipschitz interface,in finite energy norms, is well posed in Fredholm sense for real frequencies. Furthermore, we give precise conditions on the material constants ε, μ and σ and the frequency ω when this transmission problem is well posed. To solve the Maxwell transmission problem, we embed Maxwell’s equations in an elliptic Dirac equation. We develop a new boundary integral method to solve the Dirac transmission problem. This method uses a boundary integral operator, the rotation operator, which factorises the double layer potential operator. We prove spectral estimates for this rotation operator in finite energy norms using Hodge decompositions on weakly Lipschitz domains. To ensure that solutions to the Dirac transmission problem indeed solve Maxwell’s equations, we introduce an exterior/interior derivative operator acting in the trace space. By showing that this operator commutes with the two basic reflection operators, we are able to prove that the Maxwell transmission problem is well posed. We also prove well-posedness for a class of oblique Dirac transmission problems with a strongly Lipschitz interface, in the L_2 space on the interface. This is shown by employing the Rellich technique, which gives angular spectral estimates on the rotation operator.
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Perez, Thomas. "Problèmes d'algèbre extérieure liés au calcul de fonctions d'ondes électroniques produits de géminales." Thesis, Université Côte d'Azur, 2020. http://www.theses.fr/2020COAZ4060.

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En chimie quantique, les fonctions d'ondes électroniques peuvent être vues comme des multivecteurs ; les problèmes se traduisent par conséquent en langage mathématique grâce à l'algèbre extérieure.Nous rappelons en premier lieu certains résultats sur l'algèbre extérieure d'un espace de Hilbert concernant les produits extérieur et intérieur qui s'avèrent utiles pour la chimie quantique. Dans cette même partie, une méthode pour trouver l'idéal annulateur d'un multivecteur, correspondant en physique à l'espace d'exclusion par le principe de Pauli, est présentée et cette technique sera employée dans un chapitre ultérieur.Dans un deuxième temps, nous faisons un résumé des notions clés du formalisme quantique des systèmes fermioniques et de leur expression du point de vue de l'algèbre extérieure. Nous rappelons également les principales méthodes d'approximation basées sur les fonctions d'ondes en chimie quantique. Nous introduisons par la suite des versions généralisées des concepts de séniorité et d'ionicité. Ces nombres généralisés comptent de façon respective les couches partiellement et entièrement occupées pour toute partition en couches de l'espace des orbitales. Nous construisons ensuite les opérateurs hermitiens dont les espaces propres correspondent aux fonctions d'ondes associées aux différentes valeurs de séniorité généralisée ou d'ionicité généralisée. Les nombres de séniorité généralisée permettent d'établir des hiérarchies plus fines des espaces d'interaction de configuration à l'intérieur d'une séniorité ordinaire donnée.Dans le troisième et principal chapitre, nous présentons le cheminement qui nous a conduit à proposer un nouvel ansatz de fonctions d'ondes produits de géminales où les géminales ne sont pas fortement orthogonales mais satisfont à des contraintes géométriques plus faibles pour réduire l'effort de calcul sans sacrifier l'indiscernabilité des électrons. Nos contraintes géométriques se traduisent par des équations simples impliquant les traces de produits de matrices de géminales. Dans le modèle non trivial le plus basique, un ensemble de solutions est donné par des matrices diagonales par blocs où chaque bloc est de taille 2x2 et se compose d'une matrice de Pauli ou d'une matrice diagonale, multipliée par un paramètre complexe qui est à optimiser. Avec cet ansatz simplifié pour les géminales, le nombre de termes dans le calcul des éléments matriciels des observables quantiques, comme l'hamiltonien de l'équation de Schrödinger électronique, est considérablement réduit.Enfin, dans la dernière partie, nous explicitons la programmation de notre modèle de produits de géminales dans le code “Tonto”, qui est un programme et une librairie pour la cristallographie quantique et la chimie quantique écrits dans le langage “Foo”. La validité de notre code a été testée sur le calcul de l'énergie électronique de chaînes d'hydrogène. De plus, une preuve de principe que notre ansatz donne des résultats significativement plus précis que la méthode des géminales fortement orthogonales a été établie
In quantum chemistry, the electronic wave functions can be viewed as multivectors, therefore all problems translate into mathematical language thanks to the exterior algebra.We first recall some results related to the exterior and the interior products of the exterior algebra of a Hilbert space, which prove useful for quantum chemistry. We follow by presenting a method to find the annihilator ideal of a multivector, corresponding in physics to the excluded space by the Pauli principle, and this technique will be used in a later chapter.In a second step, we provide a summary of the key notions of the quantum formalism of fermionic systems and their counterpart from the point of view of the exterior algebra. We also recall the main approximation methods based on wave functions in quantum chemistry. We then introduce generalized versions of the concepts of seniority number and ionicity. These generalized numbers count respectively the partially occupied and fully occupied shells for any partition of the orbital space into shells. The Hermitian operators whose eigenspaces correspond to wave functions of definite generalized seniority or ionicity values are built. The generalized seniority numbers afford to establish refined hierarchies of configuration interaction spaces within those of fixed ordinary seniority.In the third and main chapter, we present the way that has led us to propose a new geminal product wave function ansatz where the geminals are not strongly orthogonal but satisfy weaker geometrical constraints to lower the computational effort without sacrificing the indistinguishability of the electrons. Our geometrical constraints translate into simple equations involving the traces of products of geminal matrices. In the simplest non-trivial model, a set of solutions is given by block-diagonal matrices where each block is of size 2x2 and consists of a Pauli matrix or a diagonal matrix, multiplied by a complex parameter to be optimized. With this simplified ansatz for geminals, the number of terms in the calculation of the matrix elements of quantum observables, like the Hamiltonian of the Schrödinger electronic equation, is considerably reduced.Finally, in the last part, we explain the implementation of our geminal product model in the computer code “Tonto”, which is a program and library for quantum crystallography and quantum chemistry written in the “Foo” language. The validity of our code has been tested on the calculation of the electronic energy of hydrogen chains. Moreover, a proof of principle that our ansatz gives significantly more accurate results than the strongly orthogonal geminal method has been established
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Books on the topic "Exterior algebra"

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Yokonuma, Takeo. Tensor spaces and exterior algebra. Providence, R.I: American Mathematical Society, 1992.

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Leung, Allen Yuklun. Integral formulae in differential geometry via mixed exterior algebra. Toronto: [s.n.], 1991.

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Kirillov, Anatol N. Exterior differential algebras and flat connections on Weyl groups. Kyoto, Japan: Kyōto Daigaku Sūri Kaiseki Kenkyūjo, 2004.

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Linear algebra via exterior products. lulu.com, 2010.

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Pavan, Vincent. Exterior Algebras: Elementary Tribute to Grassmann's Ideas. Elsevier, 2017.

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Pavan, Vincent. Exterior Algebras: Elementary Tribute to Grassmann's Ideas. Elsevier, 2017.

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Yokonuma, Takeo. Tensor Spaces and Exterior Algebra (Translations of Mathematical Monographs). American Mathematical Society, 1992.

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Mann, Peter. Linear Algebra. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0037.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree of mathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactly what is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.
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Mann, Peter. Calculus of Variations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0036.

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This chapter presents an introduction to linear algebra. Classical mechanics is best understood in the language of differential geometry, which itself requires a working knowledge of the key concepts in linear algebra. This chapter walks through the required knowledge from this broad discipline and guides the reader towards the goal of the next chapter, differential geometry. Topics discussed include vector spaces, linear maps, basis sets, cobases, inner products, tensors, wedge products and exterior algebra, as well as the axioms of vector space geometry. The chapter concludes with a brief discussion of Grassmann variables, which tend to crop up when classical fermionic fields are defined.
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Mann, Peter. Differential Geometry. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0038.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree ofmathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactlywhat is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.
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Book chapters on the topic "Exterior algebra"

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Duplij, Steven, Warren Siegel, Cosmas Zachos, Euro Spallucci, Władysław Marcinek, Marco De Andrade, Ion Vancea, et al. "Exterior Algebra." In Concise Encyclopedia of Supersymmetry, 142. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/1-4020-4522-0_184.

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Yang, Kichoon. "Exterior Algebra." In Exterior Differential Systems and Equivalence Problems, 1–19. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8068-7_1.

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Rosén, Andreas. "Exterior Algebra." In Geometric Multivector Analysis, 23–71. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31411-8_2.

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Herzog, Jürgen, and Takayuki Hibi. "The exterior algebra." In Monomial Ideals, 75–93. London: Springer London, 2011. http://dx.doi.org/10.1007/978-0-85729-106-6_5.

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Shafarevich, Igor R., and Alexey O. Remizov. "The Exterior Product and Exterior Algebras." In Linear Algebra and Geometry, 349–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-30994-6_10.

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Falb, Peter. "Exterior Algebra and Grassmannians." In Methods of Algebraic Geometry in Control Theory: Part II, 143–60. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1564-6_9.

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Yomdin, Yosef, and Georges Comte. "6. Some Exterior Algebra." In Lecture Notes in Mathematics, 75–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-40960-1_6.

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Sontz, Stephen Bruce. "The Braided Exterior Algebra." In Universitext, 127–37. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-15829-7_9.

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Falb, Peter. "Exterior Algebra and Grassmannians." In Methods of Algebraic Geometry in Control Theory: Part II, 143–60. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-96574-1_8.

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Sontz, Stephen Bruce. "Exterior Algebra and Differential Forms." In Universitext, 59–79. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14765-9_5.

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Conference papers on the topic "Exterior algebra"

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Guay, M., P. J. McLellan, and D. W. Bacon. "Computer algebra methods for feedback linearization using an exterior calculus framework." In Proceedings of 16th American CONTROL Conference. IEEE, 1997. http://dx.doi.org/10.1109/acc.1997.610653.

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ABRAMOV, V., and N. BAZUNOVA. "ALGEBRA OF DIFFERENTIAL FORMS WITH EXTERIOR DIFFERENTIAL d 3 = 0 IN DIMENSION ONE." In Proceedings of the Second International Symposium. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777850_0018.

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ABRAMOV, V., and N. BAZUNOVA. "EXTERIOR CALCULUS WITH d3 = 0 ON A FREE ASSOCIATIVE ALGEBRA AND REDUCED QUANTUM PLANE." In Proceedings of XIV Max Born Symposium. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812793263_0001.

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Reports on the topic "Exterior algebra"

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Histova, Elitza. Hilbert Series and Invariants in Exterior Algebras. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, February 2020. http://dx.doi.org/10.7546/crabs.2020.02.02.

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