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تسجيل مستخدم جديدCohomology and Deformations of left-symmetric Rinehart Algebras
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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 $mathcal O$-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 $mathcal O$-operators and Nijenhuis operators on left-symmetric Rinehart algebras.
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