Infinitesimal Hom-bialgebras and Hom-Lie bialgebras

Abstract

We study the Hom-type generalization of infinitesimal bialgebras, called infinitesimal Hom-bialgebras. In particular, we consider infinitesimal Hom-bialgebras arising from quivers, the sub-classes of coboundary and quasi-triangular infinitesimal Hom-bialgebras, the associative Hom-Yang-Baxter equation, and homological perturbation of the comultiplications in infinitesimal Hom-bialgebras. The relationships between infinitesimal Hom-bialgebras, Hom-Lie bialgebras, and the classical Hom-Yang-Baxter equation are also studied.

arXiv comment35 pages

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Cited by in corpus (7)

• On n-ary Hom-Nambu and Hom-Nambu-Lie algebras
• Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras
• On n-ary Hom-Nambu and Hom-Maltsev algebras
• Hom-power associative algebras
• Manin triples and quasitriangular structures of Hom-Poisson bialgebras
• A new approach to hom-Lie bialgebras
• Rota-Baxter systems on Hom-associative algebras and covariant Hom-bialgebras