Expansions of Algebras and Superalgebras and Some Applications |
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| Authors: | J. A. de Azcárraga J. M. Izquierdo M. Picón O. Varela |
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| Affiliation: | (1) Departamento de Física Teórica e IFIC, Universidad de Valencia, 46100 Burjassot (Valencia), Spain;(2) Departamento de Física Teórica, Universidad de Valladolid, 47011 Valladolid, Spain;(3) INFN Sezione di Padova and Dipartimento di Fisica “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy;(4) Theoretical Physics Group, The Blackett Laboratory, Imperial College, London, SW7 2AZ, UK |
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| Abstract: | After reviewing the three well-known methods to obtain Lie algebras and superalgebras from given ones, namely, contractions, deformations and extensions, we describe a fourth method recently introduced, the expansion of Lie (super)algebras. Expanded (super)algebras have, in general, larger dimensions than the original algebra, but also include the ?nönü–Wigner and generalized IW contractions as a particular case. As an example of a physical application of expansions, we discuss the relation between the possible underlying gauge symmetry of eleven-dimensional supergravity and the superalgebra osp(1|32). |
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