Expansions of algebras and superalgebras and some applications
J.A. de Azcarraga, J.M. Izquierdo, M. Picon, O. Varela

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).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
