On Rings of Differential Rota-Baxter Operators

TL;DR

This paper develops a framework for operator rings induced by derivations or Rota-Baxter operators, applying it to polynomial rings to create integro-differential analogs of Weyl algebras, analyzed via noncommutative algebra techniques.

Contribution

It introduces a new class of operator rings and modules using operated algebra language, extending classical algebraic structures to include Rota-Baxter and differential operators.

Findings

Construction of operator rings from derivations and Rota-Baxter operators

Application to univariate polynomial rings leading to integro-differential Weyl analogs

Analysis using skew polynomial rings and noncommutative Groebner bases

Abstract

Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying the general framework to univariate polynomials, one is led to the integro-differential analogs of the classical Weyl algebra. These are analyzed in terms of skew polynomial rings and noncommutative Groebner bases.