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arXiv · 2305.16425

Deformations and Cohomology of restricted Lie-Rinehart algebras in positive characteristic

Quentin Ehret·Abdenacer Makhlouf
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Abstract

The main purpose of this paper is to study restricted formal deformations of restricted Lie-Rinehart algebras in positive characteristic $p$. For $p>2$, we discuss the deformation theory and show that deformations are controlled by the restricted cohomology introduced by Evans and Fuchs. Furthermore, for $p=2$, we introduce a new cohomology complex and show that it fits with the deformation theory of restricted Lie-Rinehart algebras in characteristic 2. In particular, we study the structure and cohomology of restricted Heisenberg algebras.

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Quentin Ehret, Abdenacer Makhlouf. 2023-05-25. Deformations and Cohomology of restricted Lie-Rinehart algebras in positive characteristic. https://arxiv.org/abs/2305.16425

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