Monomial Rota-Baxter and averaging operators on $F[x, x^{-1}]$

Artem Khodzitskii

Monomial Rota-Baxter and averaging operators on $F[x, x^{-1}]$

Rings and Algebras 2026-07-31 v1

Authors: Artem Khodzitskii

Abstract

The study of Rota-Baxter operators on the polynomial algebra in one variable was initiated by S.H. Zheng, L. Guo, and M. Rosenkranz (2015). Monomial Rota-Baxter operators on $F[x]$ were classified in 2016, while monomial averaging operators on $F[x]$ and $F_0[x]$ were classified in 2024. In the current work, we continue the study of these operators on Laurent polynomial algebra $F[x, x^{-1}]$ over a field of arbitrary characteristic.

Keywords

Rota-Baxter operators averaging operators monomial operators Laurent polynomial algebra classification

Cite

@article{arxiv.2607.29312,
  title  = {Monomial Rota-Baxter and averaging operators on $F[x, x^{-1}]$},
  author = {Artem Khodzitskii},
  journal= {arXiv preprint arXiv:2607.29312},
  year   = {2026}
}

Comments

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