# Deformations and Homotopy Theory of Relative Rota–Baxter Lie Algebras

@article{Lazarev2020DeformationsAH, title={Deformations and Homotopy Theory of Relative Rota–Baxter Lie Algebras}, author={Andrey Lazarev and Yunhe Sheng and Rong Tang}, journal={Communications in Mathematical Physics}, year={2020} }

We determine the $$L_\infty $$
L
∞
-algebra that controls deformations of a relative Rota–Baxter Lie algebra and show that it is an extension of the dg Lie algebra controlling deformations of the underlying $$\mathsf {Lie}\mathsf {Rep}$$
Lie
Rep
pair by the dg Lie algebra controlling deformations of the relative Rota–Baxter operator. Consequently, we define the cohomology of relative Rota–Baxter Lie algebras and relate it to their infinitesimal deformations. A large class of…

## 31 Citations

Representations and cohomologies of relative Rota-Baxter Lie algebras and applications

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A Rota-Baxter Lie algebra gT is a Lie algebra g equipped with a Rota-Baxter operator T : g → g. In this paper, we consider non-abelian extensions of a Rota-Baxter Lie algebra gT by another…

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