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

2026/07/31 by Artem Khodzitskii
Mathematics · #math.RA #msc:16W99

paper · pdf

11 p

arxiv created 2026/07/31 · arxiv updated 2026/08/03

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 F₀[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.

Citations

• Linear-in-degree monomial Rota-Baxter of weight zero and averaging operators on F[x, y] and F₀[x, y]
• The integro-differential closure of a commutative differential ring
• Monomial Rota-Baxter operators of nonzero weight on F[x,y] coming from averaging operators
• Modules of polynomial Rota-Baxter Algebras and matrix equations
• Representations of Polynomial Rota-Baxter Algebras
• Representations of polynomial Rota–Baxter algebras
• Classification of monomial Rota-Baxter operators on k[x]
• Averaging algebras, Schröder numbers, rooted trees and operads
• An Algebraic Study of Averaging Operators