UC Santa Cruz

We introduce the notion of space of correlation functions associated with three modules $M^1, M^2$, and $M^3$ over a vertex operator algebra $V$. By studying the relations between the space of correlation functions with the space of intertwining operators and the bi-modules over Zhu's algebra $A(V)$, we prove a generalized version of the fusion rules theorem for vertex operator algebras. We also give the analog of Rota-Baxter operators for vertex operator algebras as a generalization of the Rota-Baxter operators for Lie algebras. We find some particular types of sub-algebras of the lattice vertex operator algebra $V_L$ to give examples of such operators. Using a general version of Rota-Baxter operators of vertex operator algebra, we find a tensor form of the Yang-Baxter equations for vertex operator algebras that generalizes the classical Yang-Baxter equation for Lie algebras.