Rota-Baxter operators on groups

DOI10.1007/S12044-023-00723-9arXiv2103.01848MaRDI QIDQ6361957

Vsevolod Yur'evich Gubarev, V. G. Bardakov

Publication date: 2 March 2021

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.

Mathematics Subject Classification ID

Simple groups: sporadic groups (20D08) Yang-Baxter equations and Rota-Baxter operators (17B38)

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