# Maxwell Superalgebras and Abelian Semigroup Expansion

Source: [Maxwell Superalgebras and Abelian Semigroup Expansion](<https://www.sota2.com/research/paper/68fa2d8e1e209131ce85a19b>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T03:24:05.390Z

Authors: P.K. Concha, E.K. Rodr\\'iguez

Published: 2014-05-06T16:05:27.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1405.1334>)

[PDF](<https://arxiv.org/pdf/1405.1334.pdf>)