  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.
