Monomial Rota–Baxter operators on free commutative non-unital algebra

Abstract

A Rota-Baxter operator defined on the polynomial algebra is called monomial if it maps each monomial to a monomial with some coefficient. We classify monomial Rota-Baxter operators defined on the algebra of polynomials in one variable without constant term. We also describe injective monomial Rota--Baxter operators of nonzero weight on the algebra of polynomials in several variables without constant term.