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- Title
Post-Hopf algebras, relative Rota-Baxter operators and solutions to the Yang-Baxter equation.
- Authors
Yunnan Li; Yunhe Sheng; Rong Tang
- Abstract
In this paper, first, we introduce the notion of post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and the fact that there is naturally a post-Hopf algebra structure on the universal enveloping algebra of a post-Lie algebra. A novel property is that a cocommutative post-Hopf algebra gives rise to a generalized Grossman-Larson product, which leads to a subadjacent Hopf algebra and can be used to construct solutions to the Yang-Baxter equation. Then, we introduce the notion of relative Rota-Baxter operator on Hopf algebras. A cocommutative post-Hopf algebra gives rise to a relative Rota-Baxter operator on its subadjacent Hopf algebra. Conversely, a relative Rota-Baxter operator also induces a post-Hopf algebra. Finally, we show that relative Rota-Baxter operators give rise to matched pairs of Hopf algebras. Consequently, post-Hopf algebras and relative Rota-Baxter operators give solutions to the Yang-Baxter equation in certain cocommutative Hopf algebras.
- Subjects
YANG-Baxter equation; HOPF algebras; UNIVERSAL algebra; ALGEBRA; OPERATOR algebras; LIE algebras
- Publication
Journal of Noncommutative Geometry, 2024, Vol 18, Issue 2, p605
- ISSN
1661-6952
- Publication type
Article
- DOI
10.4171/JNCG/537