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Expansions of algebras and superalgebras and some applications

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arxiv hep-th/0703017 v1 pith:4ML4CHJR submitted 2007-03-02 hep-th math-phmath.GMmath.GRmath.MP

Expansions of algebras and superalgebras and some applications

classification hep-th math-phmath.GMmath.GRmath.MP
keywords algebrascontractionsexpansionssupersuperalgebrasalgebraapplicationapplications
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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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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Cited by 2 Pith papers

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