On classification and deformations of Lie-Rinehart superalgebras

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 $\dim (A)\le 2$ and $\dim (L)\le 4$. 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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References in corpus (2)

• On Classification of Finite-Dimensional Superbialgebras and Hopf Superalgebras
• Representations of Homotopy Lie-Rinehart Algebras