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Structure theory of Clifford-Weyl algebras and representations of ortho-symplectic Lie superalgebras | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 8، دوره 6، شماره 1، 2025، صفحه 79-96 اصل مقاله (485.39 K) | ||
| نوع مقاله: Short Contribution | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2023.22595.1192 | ||
| نویسنده | ||
| Nasser Boroojerdian* | ||
| Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran | ||
| چکیده | ||
| In this article, the structure of the Clifford-Weyl superalgebras and their associated Lie superalgebras will be investigated. These superalgebras have a natural supersymmetric inner product which is invariant under their Lie superalgebra structures. The Clifford-Weyl superalgebras can be realized as tensor product of the algebra of alternating and symmetric tensors respectively, on the even and odd parts of their underlying superspace. For Physical applications in elementary particles, we add star structures to these algebras and investigate the basic relations. Ortho-symplectic Lie algebras are naturally present in these algebras and their representations on these algebras can be described easily. | ||
| کلیدواژه‌ها | ||
| Superspace؛ Bilinear form؛ Exterior algebra؛ Symmetric algebra؛ Star structure؛ Representation | ||
| مراجع | ||
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[1] C. Carmeli, L. Caston, and R. Fioresi, Mathematical foundations of supersymmetry, EMS Series of Lectures in Mathematics, European Mathematical Society (EMS), Z¨urich, 2011. [2] R. J. Farmer, Orthosymplectic superalgebras in mathematics and science, PhD thesis, University Of Tasmania, 1984. [3] B. Gording, A novel approach to particle representations, arXiv preprint arXiv:2005.06974, (2020). [4] W. Greub, Multilinear Algebra, Universitext (UTX), Springer New York, NY, 1978. [5] J. T. Hartwig and V. Serganova, Clifford and Weyl superalgebras and spinor representations, Transform. Groups, 25 (2020), pp. 1185–1207. [6] V. G. Kac, Lie superalgebras, Advances in Math., 26 (1977), pp. 8–96. [7] A. Kirillov, Jr., An introduction to Lie groups and Lie algebras, vol. 113 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 2008. [8] P. Renaud, Clifford algebras lecture notes on applications in physics, 2020. [9] V. S. Varadarajan, Supersymmetry for mathematicians: an introduction, vol. 11 of Courant Lecture Notes in Mathematics, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2004. [10] P. Woit, Weyl and clifford algebras, in Quantum Theory, Groups and Representations: An Introduction, Springer International Publishing, Cham, 2017, pp. 365–372. | ||
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