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.

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

References in corpus (6)

• Expanding Lie (super)algebras through abelian semigroups
• Generalized cosmological term from Maxwell symmetries
• Expansions of algebras and superalgebras and some applications
• Deformations of Maxwell algebra and their Dynamical Realizations
• Eleven-Dimensional Gauge Theory for the M Algebra as an Abelian Semigroup Expansion of osp(32|1)
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Cited by in corpus (11)

• N=1 Supergravity and Maxwell superalgebras
• Minimal D=4 supergravity from the superMaxwell algebra
• Non-Relativistic Gravity Theory based on an Enlargement of the Extended Bargmann Algebra
• Generalized Pure Lovelock Gravity
• $\mathcal{N}$-extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions
• Inönü-Wigner Contraction and $D=2+1$ Supergravity
• On the Supersymmetric Extension of Gauss-Bonnet like Gravity
• An Analytic Method for $S$-Expansion involving Resonance and Reduction
• Hypersymmetric extensions of Maxwell Chern-Simons gravity in (2+1) dimensions
• Resonant superalgebras and $\mathcal{N}=1$ supergravity theories in three spacetime dimensions
• Generalization of extended Lie algebras by expansions of extended de Sitter algebra, in four-dimensions