Quantization of Lie bialgebras, V

TL;DR

This paper extends the theory of quantum vertex operator algebras by defining their structure within formal deformation theory and constructing examples from various R-matrices, including rational, trigonometric, and elliptic types.

Contribution

It introduces the notion of quantum vertex operator algebras in deformation theory and provides explicit constructions from different R-matrices, enriching the algebraic framework.

Findings

Constructed quantum vertex operator algebras from rational, trigonometric, and elliptic R-matrices.

Identified the quantum current of Reshetikhin and Semenov-Tian-Shansky as a fundamental vertex operator.

Extended the algebraic understanding of quantum deformations of affine vertex operator algebras.

Abstract

This paper is a continuation of "Quantization of Lie bialgebras I-IV". The goal of this paper is to define and study the notion of a quantum vertex operator algebra in the setting of the formal deformation theory and give interesting examples of such algebras. In particular, we construct a quantum vertex operator algebra from a rational, trigonometric, or elliptic R-matrix, which is a quantum deformation of the affine vertex operator algebra. The simplest vertex operator in this algebra is the quantum current of Reshetikhin and Semenov-Tian-Shansky.