arXiv subjects

Viktor N. Zhelaybin

Publications and source records attributed to Viktor N. Zhelaybin.

2 recordsLinked to original sources

arXiv2024

Algebra, group, and Hopf Rota-Baxter operators

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 $H_4$, that is 4-dimension non--cocommutative Hopf algebra.

math.RA↗

arXiv2024

Lie Rota--Baxter operators on the Sweedler algebra $H_4$

If $A$ is an associative algebra, then we can define the adjoint Lie algebra $A^{(-)}$ and Jordan algebra $A^{(+)}$. It is easy to see that any associative Rota--Baxter operator on $A$ induces a Lie and Jordan Rota--Baxter operator on $A^{(-)}$ and $A^{(+)}$ respectively. Are there Lie (Jordan) Rota--Baxter operators, which are not associative Rota--Baxter operators? In the present article we are studying these questions for the Sweedler algebra $H_4$, that is a 4-dimension non-commutative Hopf algebra. More precisely, we describe the Rota--Baxter operators on Lie algebra on the adjoint Lie algebra $H_4^{(-)}$.

math.GR↗