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arXiv · 1610.01477

Hom-Lie-Rinehart Algebras

Ashis Mandal·Satyendra Kumar Mishra
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Abstract

We introduce hom-Lie-Rinehart algebras as an algebraic analogue of hom-Lie algebroids, and systematically describe a cohomology complex by considering coefficient modules. We define the notion of extensions for hom-Lie-Rinehart algebras. In the sequel, we deduce a characterisation of low dimensional cohomology spaces in terms of the group of automorphisms of certain abelian extension and the equivalence classes of those abelian extensions in the category of hom-Lie-Rinehart algebras, respectively. We also construct a canonical example of hom-Lie-Rinehart algebra associated to a given Poisson algebra and an automorphism.

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BibTeXRIS

Ashis Mandal, Satyendra Kumar Mishra. 2016-10-05. Hom-Lie-Rinehart Algebras. https://arxiv.org/abs/1610.01477

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