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arXiv · 2007.06053

Rota-Baxter systems on Hom-associative algebras and covariant Hom-bialgebras

Apurba Das
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Abstract

Rota-Baxter systems were introduced by Brzezi\'{n}ski as a generalization of Rota-Baxter operators that are related to dendriform structures, associative Yang-Baxter pairs and covariant bialgebras. In this paper, we define Rota-Baxter systems on Hom-associative algebras and show how they induce Hom-dendriform structures and weak pseudotwistors on the underlying Hom-associative algebra. We introduce Hom-Yang-Baxter pairs and a notion of covariant Hom-bialgebra. Given a Hom-Yang-Baxter pair, we construct a twisted Rota-Baxter system and a (quasitriangular) covariant Hom-bialgebra. Finally, we consider perturbations of the coproduct in a covariant Hom-bialgebra.

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Apurba Das. 2020-07-12. Rota-Baxter systems on Hom-associative algebras and covariant Hom-bialgebras. https://arxiv.org/abs/2007.06053

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