On Rota--Baxter operators on finite simple groups of Lie type

2025/09/05 by Galt, Alexey, Gubarev, Vsevolod
#20D06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2509.04961

Abstract

Rota--Baxter operators on groups were introduced by L. Guo, H. Lang, Yu. Sheng in 2020. In 2023, V. Bardakov and the second author showed that all Rota--Baxter operators on simple sporadic groups are splitting, i. e. they correspond to exact factorizations of groups. In 2024, the authors of the current paper described all non-splitting Rota--Baxter operators on alternating groups. Now we describe Rota--Baxter operators on finite simple exceptional groups of Lie type and projective special linear groups of degree two.

Citations

• Rota-Baxter operators on compact simple Lie groups and algebras
• On the integration of relative Rota-Baxter Lie algebras
• Maps, simple groups, and arc-transitive graphs
• Rota-Baxter operators on dihedral and alternating groups
• Rota-Baxter operators on groups
• Rota-Baxter operators on cocommutative Hopf algebras
• Double Poisson brackets on free associative algebras

Related

• Rota-Baxter operators on groups
• Rota-Baxter operators on dihedral and alternating groups
• Rota-Baxter operators on compact simple Lie groups and algebras
• Rota-Baxter groups with weight zero and integration on topological groups
• Some properties of relative Rota--Baxter operators on groups