Cohomology and Deformations of left-symmetric Rinehart Algebras

DOI10.46298/CM.12656arXiv2010.00335MaRDI QIDQ6504076

Sami Mabrouk, A. Ben Hassine, Taoufik Chtioui, Mohamed Elhamdadi

Abstract: We introduce a notion of left-symmetric Rinehart algebras, which is a generalization of a left-symmetric algebras. The left multiplication gives rise to a representation of the corresponding sub-adjacent Lie-Rinehart algebra. We construct left-symmetric Rinehart algebra from $mathcalO$-operators on Lie-Rinehart algebra. We extensively investigate representations of a left-symmetric Rinehart algebras. Moreover, we study deformations of left-symmetric Rinehart algebras, which is controlled by the second cohomology class in the deformation cohomology. We also give the relationships between $mathcalO$-operators and Nijenhuis operators on left-symmetric Rinehart algebras.

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Representation theory of lattices (06B15) Local deformation theory, Artin approximation, etc. (14B12)

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