Associative Rota--Baxter operators on the Sweedler algebra $H_4$
Rings and Algebras
2026-02-04 v1
Abstract
In this paper, we classify all Rota--Baxter operators on the Sweedler algebra up to conjugation and dualization. Modulo algebra (anti)automorphisms of , we first describe its subalgebras and then analyse the kernel of a Rota--Baxter operator. The classification is carried out according to the dimension of this kernel, yielding a complete description of such operators. A complete list of operators is given in the theorem of the final section.
Cite
@article{arxiv.2602.03133,
title = {Associative Rota--Baxter operators on the Sweedler algebra $H_4$},
author = {Maxim V. Podkorytov},
journal= {arXiv preprint arXiv:2602.03133},
year = {2026}
}