Deformations and Homotopy of Rota-Baxter Operators and O-Operators on Lie Algebras

摘要

This article gives a brief introduction to some recent work on deformations and homotopy theories of Rota-Baxter operators and more generally 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 O-operators and pre-Lie algebras to the levels of deformations and homotopy.