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

Lazarev, Andrey; Sheng, Yunhe; Tang, Rong

doi:10.1090/tran/8844

Homotopy relative Rota-Baxter lie algebras, triangular $L_\infty$-bialgebras and higher derived brackets
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by Andrey Lazarev, Yunhe Sheng and Rong Tang;

Trans. Amer. Math. Soc. 376 (2023), 2921-2945

DOI: https://doi.org/10.1090/tran/8844

Published electronically: January 12, 2023

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Abstract:

We describe $L_\infty$-algebras governing triangular $L_\infty$-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.

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