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Expansions of algebras and superalgebras and some applications

AuthorsAzcárraga, José A. de ; Izquierdo, José Manuel; Picón, M.; Varela, Óscar
KeywordsInonu-Wigner contractions
Continuous graded contractions
Lie algebras
Group representations
Topological extensions
Extended superspaces
Deformation theory
D=11 Supergravity
BPS States
Issue Date6-Jun-2007
CitationInternational Journal of Theoretical Physics 46(11): 2738-2752 (2007)
AbstractAfter 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 Inonu-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).
Description15 pages.-- PACS nrs.: 02.20.Bb, 04.65.+e, 12.60.Jv.-- ISI Article Identifier: 000250585900005.-- ArXiv pre-print available at: http://arxiv.org/abs/hep-th/0703017
Invited lecture delivered at the 'Deformations and Contractions in Mathematics and Physics Workshop' (Jan 15–21, 2006, Mathematisches Forschungsinstitut Oberwolfach, Germany).-- Printed version published Nov 2007.
Publisher version (URL)http://dx.doi.org/10.1007/s10773-007-9385-3
Appears in Collections:(IFIC) Artículos
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