Quentin Ehret ; Abdenacer Makhlouf - 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) - https://doi.org/10.46298/cm.10537
On classification and deformations of Lie-Rinehart superalgebras

Authors: 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.


    Volume: Volume 30 (2022), Issue 2 (Special Issue: CIMPA School "Nonassociative Algebras and Its Applications", Madagascar 2021)
    Published on: December 27, 2022
    Accepted on: December 22, 2022
    Submitted on: December 22, 2022
    Keywords: Mathematics - Representation Theory,Mathematics - Rings and Algebras

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