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arXiv · 2107.11478

On classification and deformations of Lie-Rinehart superalgebras

Quentin Ehret·Abdenacer Makhlouf
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Abstract

The purpose of this paper is to study Lie-Rinehart superalgebras over characteristic zero fields, which are consisting of a supercommutative associative superalgebra $A$ and a Lie superalgebra $L$ that are compatible in a certain way. We discuss their structure and provide a classification in small dimensions. We describe all possible pairs defining a Lie-Rinehart superalgebra for $\dim(A)\leq 2$ and $\dim(L)\leq 4$. Moreover, we construct a cohomology complex and develop a theory of formal deformations based on formal power series and this cohomology.

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Quentin Ehret, Abdenacer Makhlouf. 2022-12-24. On classification and deformations of Lie-Rinehart superalgebras. https://doi.org/10.46298/cm.10537

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