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Artem Khodzitskii

Publications and source records attributed to Artem Khodzitskii.

3 recordsLinked to original sources
arXiv2026

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

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.

math.RA↗
arXiv2024

Monomial Rota-Baxter operators of weight zero and averaging operators on the polynomial algebra

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) non-increasing 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 RB-operator and vice versa.

math.RA↗