Quentin Ehret ; Abdenacer Makhlouf
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On classification and deformations of Lie-Rinehart superalgebras
cm:10537 -
Communications in Mathematics,
December 27, 2022,
Volume 30 (2022), Issue 2 (Special Issue: CIMPA School "Nonassociative Algebras and Its Applications", Madagascar 2021)
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https://doi.org/10.46298/cm.10537
On classification and deformations of Lie-Rinehart superalgebrasArticle
Authors: Quentin Ehret ; Abdenacer Makhlouf
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Quentin Ehret;Abdenacer Makhlouf
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.