On Rota-Baxter vertex operator algebras

Derivations play a fundamental role in the definition of vertex (operator) algebras, sometimes regarded as a generalization of differential commutative algebras. This paper studies the role played by the integral counterpart of the derivations, namely Rota-Baxter operators, in vertex (operator) algebras. The closely related notion of dendriform algebras is also defined for vertex operator algebras. It is shown that the classical relations among dendriform algebras, associative algebras, and Rota-Baxter algebras are preserved for their vertex algebra analogs.