Homotopy relative Rota-Baxter lie algebras, triangular 𝐿_{∞}-bialgebras and higher derived brackets

Abstract

We describe L ∞ L_\infty -algebras governing triangular L ∞ L_\infty -bialgebras and homotopy relative Rota-Baxter Lie algebras and establish a map between them. Our formulas are based on a functorial approach to Voronov’s higher derived brackets construction which is of independent interest.