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- W3196173003 abstract "Given a Lie algebroid with a representation, we construct a graded Lie algebra whose Maurer-Cartan elements characterize relative Rota-Baxter operators on Lie algebroids. We give the cohomology of relative Rota-Baxter operators and study infinitesimal deformations and extendability of order n deformations to order n+1 deformations of relative Rota-Baxter operators in terms of this cohomology theory. We also construct a graded Lie algebra on the space of multi-derivations of a vector bundle whose Maurer-Cartan elements characterize left-symmetric algebroids. We show that there is a homomorphism from the controlling graded Lie algebra of relative Rota-Baxter operators on Lie algebroids to the controlling graded Lie algebra of left-symmetric algebroids. Consequently, there is a natural homomorphism from the cohomology groups of a relative Rota-Baxter operator to the deformation cohomology groups of the associated left-symmetric algebroid. As applications, we give the controlling graded Lie algebra and the cohomology theory of Koszul-Vinberg structures on left-symmetric algebroids." @default.
- W3196173003 created "2021-08-30" @default.
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- W3196173003 date "2022-07-13" @default.
- W3196173003 modified "2023-09-30" @default.
- W3196173003 title "Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures" @default.
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- W3196173003 doi "https://doi.org/10.3842/sigma.2022.054" @default.
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