# 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}
}
• Published 15 August 2020
• Mathematics
• Communications in Mathematical Physics
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…
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