Monomial Rota–Baxter Operators of Weight Zero and Averaging Operators on the Polynomial Algebra
Abstract
Starting with the work S.H. Zheng, L. Guo and M. Rosenkranz (2015), Rota–Baxter operators are studied on the polynomial algebra. Injective Rota–Baxter operators of weight zero on $$F[x]$$ were described in 2021. We classify the following classes of monomial Rota–Baxter operators of weight zero on the polynomial algebra $$F[x,y]$$ and its augmentation ideal $${{F}_{0}}[x,y]$$ : (1) nonincreasing in degree that do not contain monomials in the kernel, (2) mapping all monomials to themselves with a coefficient. In the context of these sets of operators, we show how one may define a monomial averaging operator by a given Rota–Baxter operator and vice versa.
Fields of Study & Subjects
Advanced Topics in Algebra
Matrix Theory and Algorithms
Holomorphic and Operator Theory
Publication details
- Journal / source
- Russian Mathematics
- Publisher
- Kazan Federal University
- Volume
- 70
- Issue
- 4
- Pages
- 21–41
- Publication date
- 1 April 2026
- Language
- EN