On the structure of quantum vertex algebras

Abstract

© 2020 Author(s). A definition of a quantum vertex algebra, which is a deformation of a vertex algebra, was proposed by Etingof and Kazhdan in 1998 [Sel. Math. 6(1), 105-130 (2000)]. In a nutshell, a quantum vertex algebra is a braided state-field correspondence that satisfies associativity and braided locality axioms. We develop a structure theory of quantum vertex algebras, parallel to that of vertex algebras. In particular, we introduce braided n-products for a braided state-field correspondence and prove for quantum vertex algebras a version of the Borcherds identity.