Rota-Baxter operators on cocommutative Hopf algebras

2020/11/29 by Maxim Goncharov, M. E. Goncharov · 30 citations
Chemistry · Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Chemistry #Group (periodic table) #Hopf algebra #Lie algebra #Mathematics #Operator (biology) #Pure mathematics #Quantum group #Universal enveloping algebra #math.RA #msc:16S30 #msc:16T99 #msc:17B38 #msc:17B40

paper · pdf · doi:10.1016/j.jalgebra.2021.04.024

published in Journal of Algebra 582, 39-56 (Elsevier BV) · 14 pages

arxiv created 2020/11/29 · openalex publication_date 2021/05/07 · arxiv updated 2021/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

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(\mathfrakg) the universal enveloping algebra of a Lie algebra \mathfrakg, 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.

Citations

• Rota–Baxter coalgebras and Rota–Baxter bialgebras

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