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Given a Lie algebroid with a representation, we construct a graded Liealgebra whose Maurer-Cartan elements characterize relative Rota-Baxteroperators on Lie algebroids. We give the cohomology of relative Rota-Baxteroperators and study infinitesimal deformations and extendability of order $n$deformations to order $n+1$ deformations of relative Rota-Baxter operators interms of this cohomology theory. We also construct a graded Lie algebra on thespace of multi-derivations of a vector bundle whose Maurer-Cartan elementscharacterize left-symmetric algebroids. We show that there is a homomorphismfrom the controlling graded Lie algebra of relative Rota-Baxter operators onLie algebroids to the controlling graded Lie algebra of left-symmetricalgebroids. Consequently, there is a natural homomorphism from the cohomologygroups of a relative Rota-Baxter operator to the deformation cohomology groupsof the associated left-symmetric algebroid. As applications, we give thecontrolling graded Lie algebra and the cohomology theory of Koszul-Vinbergstructures on left-symmetric algebroids.

Deformations and Cohomologies of Relative Rota-Baxter Operators on Lie Algebroids and Koszul-Vinberg Structures