Rota-Baxter operators on generalized power series rings

TL;DR

This paper investigates conditions under which generalized power series rings admit Rota-Baxter operators, extending the understanding of these operators beyond Laurent series to more general algebraic structures.

Contribution

It characterizes when generalized power series rings possess Rota-Baxter operators based on the properties of the underlying ordered monoid.

Findings

Rota-Baxter operators exist on certain generalized power series rings

The structure of the ordered monoid influences the existence of Rota-Baxter operators

Connections between quantum field theory applications and algebraic structures are explored

Abstract

An important instance of Rota-Baxter algebras from their quantum field theory application is the ring of Laurent series with a suitable projection. We view the ring of Laurent series as a special case of generalized power series rings with exponents in an ordered monoid. We study when a generalized power series ring has a Rota-Baxter operator and how this is related to the ordered monoid.