Expansions of algebras and superalgebras and some applications

Details Expansions of algebras and superalgebras and some applications Expansions of algebras and superalgebras and some applications

2007-03-02

arxiv.org/abs/hep-th/0703017v1

Int.J.Theor.Phys.46:2738-2752,2007

Physics

High Energy Physics

High Energy Physics - Theory

Invited lecture delivered at the 'Deformations and Contractions in Mathematics and Physics Workshop', 15-21 January 2006, Math

Scientific paper

10.1007/s10773-007-9385-3

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 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).

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