Quantization of Lie bialgebras, V

1998/08/28 by Pavel Etingof, David Kazhdan, Etingof, Pavel +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.math/9808121

22 pages, amstex. This is the 5-th part of the Quantization series, starting from q-alg/9506005

arxiv created 1998/08/28 · openalex publication_date 1998/08/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Quantization of Lie bialgebras, part VI: quantization of generalized Kac-Moody algebras
• CONSTRUCTING QUANTUM VERTEX ALGEBRAS

Related

• Some Classical and Quantum Algebras
• Deformation quantization of vertex Poisson algebras
• H_D-Quantum Vertex Algebras and Bicharacters
• Factorisation quantum groups
• Associating quantum vertex algebras to certain deformed Heisenberg Lie algebras