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CLASSIFICATION OF ROTA-BAXTER OPERATORS ON D8
Pages : [153] - [193]
Received : Received October 19, 2023; Revised December 27, 2023
Communicated by : Professor Suayip Yuzbasi
Abstract
Rota-Baxter operators on Lie groups were introduced recently as integrals of Rota-Baxter operators on Lie algebras with applications to integrable systems. In [5], Das and Rathee listed Rota-Baxter operators on the dihedral group D8 which are extension of some homomorphism on the unique cyclic subgroup with order 4 of D8. The aim of this paper is to classify Rota-Baxter operators on D8. With the aid of Matlab procedures, it is proved that there exist 56 Rota-Baxter operators on D8 including 18 splitting Rota-Baxter operators and 28 Rota-Baxter operators that are group endomorphisms. The Rota-Baxter endomorphisms form a semigroup with respect to composition.
Keywords
Rota-Baxter operator, dihedral group, Rota-Baxter endomorphism.