Rota-Baxter operators on cocommutative Hopf algebras

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Abstract

In this paper, we introduce and study the notion of a Rota-Baxter operator on a cocommutative Hopf algebra that generalizes notions of a Rota-Baxter operator on a group and a Rota-Baxter operator of weight 1 on a Lie algebra. We show that every Rota-Baxter operator (of weight 1) on a Lie algebra g (resp., on a group G) can be uniquely extended to a Rota-Baxter operator on the universal enveloping algebra U(g) (resp., on the group algebra F[G]).

Original languageEnglish
Pages (from-to)39-56
Number of pages18
JournalJournal of Algebra
Volume582
DOIs
Publication statusPublished - 15 Sep 2021

Keywords

  • Cocommutative Hopf algebra
  • Rota-Baxter group
  • Rota-Baxter Lie algebra
  • Rota—Baxter operator

OECD FOS+WOS

  • 1.01 MATHEMATICS

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