2024/05/14 by Valeriy G. Bardakov, Bardakov, Valeriy G., Igor Nikonov +3
Computer Science · Mathematics · Physics and Astronomy · #16T05 #17B38 #Advanced Differential Geometry Research #Advanced Topics in Algebra #FOS: Mathematics #Group Theory (math.GR) #Matrix Theory and Algorithms #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2405.08291
openalex publication_date 2024/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 H4, 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 H4(-).