$\{\unicode[STIX]{x1D70E}, \unicode[STIX]{x1D70F}\}$-Rota–Baxter Operators, Infinitesimal Hom-bialgebras and the Associative (Bi)Hom-Yang–Baxter Equation. Issue 2 (7th January 2019)

• Record Type: Journal Article
• Authors: Liu, Ling; Makhlouf, Abdenacer; Menini, Claudia; Panaite, Florin
• Is Part Of: Canadian mathematical bulletin =. Volume 62:Issue 2(2019)
• Page Start: 355
• Page End: 372
• Publication Date: 2019-01-07
• Subjects: 15A04, -- 17A99, -- 17D99; Rota–Baxter operator, -- Hom-pre-Lie algebra, -- infinitesimal Hom-bialgebra, -- associative (Bi)Hom-Yang–Baxter equation; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2018-028-8
• Languages: English
• ISSNs: 0008-4395

Abstract

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.