Deformations and homotopy of Rota-Baxter operators and $\mathcal{O}$-operators on Lie algebras

Abstract

This article gives a brief introduction to some recent work on deformation and homotopy theories of Rota-Baxter operators and more generally $\mathcal{O}$-operators on Lie algebras, by means of the differential graded Lie algebra approach. It is further shown that these theories lift the existing connection between $\mathcal{O}$-operators and pre-Lie algebras to the levels of deformations and homotopy.

arXiv comment8 pages

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Cited by in corpus (1)

• A survey on deformations, cohomologies and homotopies of relative Rota-Baxter Lie algebras