A. Ben Hassine ; T. Chtioui ; M. Elhamdadi ; S. Mabrouk
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Cohomology and Deformations of left-symmetric Rinehart Algebras
cm:12656 -
Communications in Mathematics,
April 22, 2024,
Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024")
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https://doi.org/10.46298/cm.12656
Cohomology and Deformations of left-symmetric Rinehart AlgebrasArticle
Authors: A. Ben Hassine ; T. Chtioui ; M. Elhamdadi ; S. Mabrouk
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A. Ben Hassine;T. Chtioui;M. Elhamdadi;S. Mabrouk
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 O-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 O-operators and Nijenhuis
operators on left-symmetric Rinehart algebras.