Expansions of algebras and superalgebras and some applications

TL;DR

The paper introduces a new method called expansion for Lie (super)algebras, expanding their dimensions and encompassing previous methods like contractions, with applications in theoretical physics such as supergravity.

Contribution

It presents the expansion method for Lie (super)algebras, expanding their structure and unifying previous contraction techniques, with an application to eleven-dimensional supergravity.

Findings

Expanded superalgebras have larger dimensions than original.

Expansion includes Inonu-Wigner contractions as a special case.

Application to supergravity shows potential for gauge symmetry analysis.

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 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).