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arXiv · 1802.08707

On Degenerations of Lie Superalgebras

María Alejandra Alvarez·Isabel Hernández
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Abstract

We give necessary conditions for the existence of degenerations between two complex Lie superalgebras of dimension $(m,n)$. As an application, we study the variety $\mathcal{LS}^{(2,2)}$ of complex Lie superalgebras of dimension $(2,2)$. First we give the algebraic classification and then obtain that $\mathcal{LS}^{(2,2)}$ is the union of seven irreducible components, three of which are the Zariski closures of rigid Lie superalgebras. As byproduct, we obtain an example of a nilpotent rigid Lie superalgebra, in contrast to the classical case where no example is known.

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María Alejandra Alvarez, Isabel Hernández. 2018-02-23. On Degenerations of Lie Superalgebras. https://arxiv.org/abs/1802.08707

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