Algebras constructed by Rota-Baxter operators

TL;DR

This paper investigates the algebraic structures formed by associative commutative algebras equipped with Rota-Baxter operators, deriving identities for the new algebraic operations induced by these operators.

Contribution

It introduces and characterizes identities of algebras constructed via Rota-Baxter operators on associative commutative algebras.

Findings

Identifies algebraic identities for $AR=(A, \, \circ)$ with $a \circ b= a R(b)$

Provides a framework for understanding Rota-Baxter induced algebra structures

Lays groundwork for further algebraic and combinatorial applications

Abstract

For associative commutative algebras $A$ with Rota-Baxter operator $R$ identities of the algebra $AR=(A,\circ)$, where $a\circ b= aR(b),$ are found.