  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.
