Quasitriangular covariant monoidal BiHom-bialgebras, associative monoidal BiHom-Yang–Baxter equations and Rota–Baxter paired monoidal BiHom-modules
Volume 161 / 2020
Colloquium Mathematicum 161 (2020), 189-221
MSC: 16T05, 16W99.
DOI: 10.4064/cm7993-9-2019
Published online: 20 March 2020
Abstract
In this paper, we mainly introduce the notion of covariant monoidal BiHom-bialgebra, which is an extended form of infinitesimal monoidal BiHom-bialgebra. We focus on the characterizations of quasitriangular covariant monoidal BiHom-bialgebras, which leads to the concept of associative monoidal BiHom-Yang–Baxter pair and the associative monoidal BiHom-Yang–Baxter equation. We also investigate the relations among quasitriangular covariant monoidal BiHom-bialgebras, Rota–Baxter monoidal BiHom-systems, monoidal BiHom-pre-Lie algebras and monoidal BiHom-dendriform algebras. On the other hand, we consider Rota–Baxter paired monoidal BiHom-modules and also list some basic properties and examples of Rota–Baxter paired monoidal BiHom-modules.
