2024/12/10 by Valeriy G. Bardakov, Bardakov, Valeriy G., Igor Nikonov +3
Mathematics · Computer Science · #Advanced Topics in Algebra #Matrix Theory and Algorithms #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2412.07158
We know definition of Rota--Baxter operators on different algebraic systems. For examples, on groups, on algebras, on Hopf algebras. On some algebraic systems it is possible to define different types of Rota--Baxter operators. For example, on group algebra it is possible to define Rota--Baxter operator as on associative algebra, group Rota--Baxter operator and Rota--Baxter operator as on a Hopf algebra. We are investigating the following question: What are connections between these operators? We are studying these questions for the Sweedler algebra H4, that is 4-dimension non--cocommutative Hopf algebra.