Rota-Baxter co-operators on commutative Hopf algebras

Abstract

In this paper, we mainly research Rota-Baxter co-operators on commutative Hopf algebras. We get a new Hopf algebra and some Hopf co-braces via Rota-Baxter co-operators on commutative Hopf algebras. Finally, we generalize Rota-Baxter co-operators to relative Rota-Baxter co-operators of Hopf algebras, construct a Hopf cobrace by a relative Rota-Baxter co-operator of commutative Hopf algebra, and establish the relation of relative Rota-Baxter co-operators and bijective 1-cocycles.

KEYWORDS:

• Bjective 1-cocycle
• Hopf algebra
• Hopf co-brace
• Rota-Baxter co-operator

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 16T05
• 16W99

Additional information

Funding

This work was supported by National Natural Science Foundation of China (12201188, 12301023), China Postdoctoral Science Foundation (2022M711076), and postdoctoral research grant in Henan Province (No. 202103090).