$\{\unicode[STIX]{x1D70E},\unicode[STIX]{x1D70F}\}$-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation

Liu, Ling ; Makhlouf, Abdenacer ; Menini, Claudia ; Panaite, Florin

Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 355-372

Résumé

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.

Détail

DOI : 10.4153/CMB-2018-028-8

Mots-clés : Rota–Baxter operator, Hom-pre-Lie algebra, infinitesimal Hom-bialgebra, associative (Bi)Hom-Yang–Baxter equation

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