Cohomology and Deformations of left-symmetric Rinehart Algebras
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 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.
Keywords
Cite
@article{arxiv.2010.00335,
title = {Cohomology and Deformations of left-symmetric Rinehart Algebras},
author = {A. Ben Hassine and T. Chtioui and M. Elhamdadi and S. Mabrouk},
journal= {arXiv preprint arXiv:2010.00335},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:1710.03749, arXiv:1312.6526, arXiv:1808.01909 by other authors