Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras

摘要

We introduce the notion of a matching Rota-Baxter algebra motivated by the recent work on multiple pre-Lie algebras arising from the study of algebraic renormalization of regularity structures [10,19]. This notion is also related to iterated integrals with multiple kernels and solutions of the associative polarized Yang-Baxter equation. Generalizing the natural connection of Rota-Baxter algebras with dendriform algebras to matching Rota-Baxter algebras, we obtain the notion of matching dendriform algebras. As in the classical case of one operation, matching Rota-Baxter algebras and matching dendriform algebras are related to matching preLie algebras which coincide with the aforementioned multiple pre-Lie algebras. More general notions and results on matching tridendriform algebras and matching PostLie algebras are also obtained. (C) 2020 Elsevier Inc. All rights reserved.