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.