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.12656Cohomology 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.
Comment: arXiv admin note: text overlap with arXiv:1710.03749, arXiv:1312.6526, arXiv:1808.01909 by other authors
Volume: Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024")
Published on: April 22, 2024
Accepted on: February 29, 2024
Submitted on: December 6, 2023
Keywords: Mathematics - Rings and Algebras, Mathematics - Representation Theory, Primary 17E05, 53D17, Secondary 14B12, 06B15