Hom-Lie-Rinehart algebras |
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Authors: | Ashis Mandal Satyendra Kumar Mishra |
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Institution: | Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, India |
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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 characterization 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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Keywords: | Cohomology of Lie- Rinehart algebras hom-algebras Lie algebroids Lie- Rinehart algebras |
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