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arXiv · 1110.3007

Cohomology of Restricted Lie-Rinehart Algebras and the Brauer Group

Ioannis Dokas
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Abstract

We give an interpretation of the Brauer group of a purely inseparable extension of exponent 1, in terms of restricted Lie-Rinehart cohomology. In particular, we define and study the category $p$-$\rm{LR}(A)$ of restricted Lie-Rinehart algebras over a commutative algebra $A$. We define cotriple cohomology groups $H_{p-LR}(L,M)$ for $L\in p$-$\rm{LR}(A)$ and $M$ a Beck $L$-module. We classify restricted Lie-Rinehart extensions. Thus, we obtain a classification theorem for regular extensions considered by Hoshschild.

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Ioannis Dokas. 2011-10-13. Cohomology of Restricted Lie-Rinehart Algebras and the Brauer Group. https://arxiv.org/abs/1110.3007

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