An alternative approach to deformations of restricted Lie-Rinehart algebras

2025/04/20 by Ehret, Quentin · 1 citation
#16W25 #17B50 #17B56 #17B60 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2504.14527

Abstract

In this paper, we develop a new approach to the deformation theory of restricted Lie-Rinehart algebras in positive characteristic, based on the deformation theory of restricted morphisms introduced in our earlier work. We provide a full cohomology complex adapted to restricted Lie-Rinehart algebras in characteristic 2, define formal deformations, study obstructions and equivalence classes, and show that these are controlled by the cohomology we introduce. In characteristic p≥ 3, we construct 2-cocycles and investigate their relationship with formal deformations. Explicit computations are given in characteristic 2 to illustrate the theory.

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• The Superization of Hochschild's Lemma and Restricted Lie-Rinehart Superalgebras

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