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

By Yi Zhang, Xing Gao, Li Guo. 2019

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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~[10,18]. 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 pre-Lie 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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/157eed589b9ccaeae9b0cdb8a2581a38a0a6e8df