Deformations of relative Rota-Baxter operators on Leibniz algebras

Abstract

In this paper, we introduce the cohomology theory of relative Rota-Baxter operators on Leibniz algebras. We use the cohomological approach to study linear and formal deformations of relative Rota-Baxter operators. In particular, the notion of Nijenhuis elements is introduced to characterize trivial linear deformations. Formal deformations and extendibility of order n deformations of a relative Rota-Baxter operator are also characterized in terms of the cohomology theory.

arXiv commentarXiv admin note: text overlap with arXiv:1803.09287

References in corpus (7)

• Renormalization in quantum field theory and the Riemann-Hilbert problem I: the Hopf algebra structure of graphs and the main theorem
• Splitting of operations, Manin products and Rota-Baxter operators
• The Embedding Tensor, Leibniz-Loday Algebras, and Their Higher Gauge Theories
• Leibniz bialgebras, relative Rota-Baxter operators and the classical Leibniz Yang-Baxter equation
• Simultaneous deformations and Poisson geometry
• Courant algebroid and Lie bialgebroid contractions
• Cohomology and Deformations of $n$-Lie algebra morphisms

Cited by in corpus (5)

• Cohomology, deformations and extensions of Rota-Baxter Leibniz algebras
• Deformations and homotopy theory of Rota-Baxter algebras of any weight
• Twisted relative Rota-Baxter operators on Leibniz algebras and NS-Leibniz algebras
• Twisted O-operators on 3-Lie algebras and 3-NS-Lie algebras
• Relative Rota-Baxter systems on Leibniz algebras