Maxwell Superalgebras and Abelian Semigroup Expansion

TL;DR

This paper extends the Abelian semigroup expansion method to derive new Maxwell superalgebras in four dimensions, including minimal and extended versions, from known superalgebras like osp(4|N), providing an alternative derivation approach.

Contribution

It demonstrates that various Maxwell superalgebras can be systematically obtained via S-expansion of osp(4|N), including new minimal and extended types, broadening the algebraic toolkit.

Findings

Derived minimal Maxwell superalgebra sM as S-expansion of osp(4|N)

Obtained N-extended Maxwell superalgebras sM(N) through S-expansion

Introduced new minimal Maxwell superalgebras sM_{m+2} via S-expansion

Abstract

The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the $S$-expansion of $\mathfrak{so}\left( 3,2\right) $ leads us to the Maxwell algebra $\mathcal{M}$. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups $S$ lead to interesting $D=4$ Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra $s\mathcal{M}$ and the $N$-extended Maxwell superalgebra $s\mathcal{M}^{\left( N\right) }$ recently found by the Maurer Cartan expansion procedure, are derived alternatively as an $S$-expansion of $\mathfrak{osp}\left( 4|N\right) $. Moreover we show that new minimal Maxwell superalgebras type $s\mathcal{M}_{m+2}$ and their $N$-extended generalization can be obtained using the $S$-expansion procedure.