Rota-Baxter operators on groups

Abstract

Theory of Rota-Baxter operators on rings and algebras has been developed since 1960. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] have defined the notion of Rota-Baxter operator on a group. We provide some general constructions of Rota-Baxter operators on a group. Given a map on a group, we study its extensions to a Rota-Baxter operator. We state the connection between Rota-Baxter operators on a group and Rota-Baxter operators on an associated Lie ring. We describe Rota-Baxter operators on sporadic simple groups.

26 p; v2: formulation of Theorem 10.1 is corrected

References in corpus (2)

• Rota-Baxter groups, skew left braces, and the Yang-Baxter equation
• From Rota-Baxter Algebras to Pre-Lie Algebras

Cited by in corpus (10)

• Rota-Baxter groups, skew left braces, and the Yang-Baxter equation
• Factorizable Lie bialgebras, quadratic Rota-Baxter Lie algebras and Rota-Baxter Lie bialgebras
• Extensions and automorphisms of Rota-Baxter groups
• Relative Rota-Baxter groups and skew left braces
• Lie theory and cohomology of relative Rota-Baxter operators
• Schur multiplier and Schur covers of relative Rota-Baxter groups
• Rota--Baxter operators and skew left brace structures over Heisenberg Group
• Cohomology and Extensions of Relative Rota-Baxter groups
• On the integration of relative Rota-Baxter Lie algebras
• Formal integration of complete Rota-Baxter Lie algebras