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$\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation
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Ling Liu, Abdenacer Makhlouf, Claudia Menini, Florin Panaite
Journal:

Canadian Mathematical Bulletin / Volume 62 / Issue 2 / June 2019

Published online by Cambridge University Press:

07 January 2019, pp. 355-372

Print publication:

June 2019
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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.