On Rota-Baxter vertex operator algebras

TL;DR

This paper explores the role of Rota-Baxter operators in vertex operator algebras, extending the algebraic framework and establishing relations with dendriform and associative algebras.

Contribution

It introduces Rota-Baxter operators into vertex operator algebras and defines dendriform structures within this context, revealing preserved classical algebraic relations.

Findings

Rota-Baxter operators are integrated into vertex operator algebras.

Dendriform algebra structures are defined for vertex operator algebras.

Classical relations among dendriform, associative, and Rota-Baxter algebras are maintained.

Abstract

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.