Classification of monomial Rota-Baxter operators on k[x]

TL;DR

This paper explicitly classifies all monomial Rota-Baxter operators on the polynomial algebra k[x], providing a comprehensive understanding of their structure and applications in mathematics and physics.

Contribution

The paper offers the first complete classification of monomial Rota-Baxter operators on k[x], advancing the theoretical understanding of these operators in algebra and related fields.

Findings

Complete classification of monomial Rota-Baxter operators on k[x]

Identification of structural properties of these operators

Potential applications in analysis and mathematical physics

Abstract

Rota-Baxter operators were introduced to solve certain analytic and combinatorial problems and then applied to many fields in mathematics and mathematical physics. The polynomial algebra $\mathbf{k}[x]$ plays a central role both in analysis and algebra. In this paper, we explicitly classified all monomial Rota-Baxter operators on $\mathbf{k}[x]$.