$\{\unicode[STIX]{x1D70E}, \unicode[STIX]{x1D70F}\}$-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation. Issue 2 (7th January 2019) - Liu, Ling; Makhlouf, Abdenacer; Menini, Claudia; Panaite, Florin
Abstract: We introduce the concept of a $\{\unicode[STIX]{x1D70E}, \unicode[STIX]{x1D70F}\}$ -Rota–Baxter operator, as a twisted version of a Rota–Baxter operator of weight zero. We show how to obtain a certain $\{\unicode[STIX]{x1D70E}, \unicode[STIX]{x1D70F}\}$ -Rota–Baxter operator from a solution of the associative (Bi)Hom-Yang–Baxter equation, and, in a compatible way, a Hom-pre-Lie algebra from an infinitesimal Hom-bialgebra.