English

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 H4H_4 up to conjugation and dualization. Modulo algebra (anti)automorphisms of H4H_4, 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.

Keywords

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}
}