Rota-Baxter operators on cocommutative Hopf algebras.

By M. Goncharov. 2020

50 citations recorded by the source corpus.

We generalize the notion of a Rota-Baxter operator on groups and the notion of a Rota-Baxter operator of weight 1 on Lie algebras and define and study the notion of a Rota-Baxter operator on a cocommutative Hopf algebra $H$. If $H=F[G]$ is the group algebra of a group $G$ or $H=U(\mathfrak{g})$ the universal enveloping algebra of a Lie algebra $\mathfrak{g}$, then we prove that Rota-Baxter operators on $H$ are in one to one correspondence with corresponding Rota-Baxter operators on groups or Lie algebras.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1dae34d21268c5b5447b75d5f1493bf1f1ea8a85

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Valeriy G. Bardakov
2. Vsevolod Gubarev

In Geometry and Topology

1. Valeriy G. Bardakov
2. Vsevolod Gubarev

In Mathematical Physics

1. Valeriy G. Bardakov
2. Vsevolod Gubarev

Citations in the corpus

• Rota—Baxter groups, skew left braces, and the Yang—Baxter equation (2021, background): “To the moment, there are few works on Rota—Baxter groups [4, 14, 19].”