Deformations and Homotopy Theory of Relative Rota–Baxter Lie Algebras

• DOI: 10.1007/s00220-020-03881-3
• Publication Date: 2020-10-04T03:46:17Z
• Authors: Andrey Lazarev; Yunhe Sheng; Rong Tang
• Keywords: Graded Lie algebra

We determine the \emph{$L_\infty$-algebra} that controls deformations of a relative Rota-Baxter Lie algebra and show it is an extension dg controlling underlying LieRep pair by operator. Consequently, we define {\em cohomology} algebras relate to their infinitesimal deformations. A large class obtained from triangular bialgebras construct map between corresponding deformation complexes. Next, notion \emph{homotopy} introduced. homotopy intimately related \emph{pre-Lie$_\infty$-algebras}.