Maxwell Superalgebras and Abelian Semigroup 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.

arXiv comment31 pages, some clarifications in the abstract,introduction and conclusion, typos corrected, a reference and acknowledgements added, accepted for publication in Nuclear Physics B

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