On the structure of quantum vertex algebras

Abstract

A definition of a quantum vertex algebra, which is a deformation of a vertex algebra, was proposed by Etingof and Kazhdan in 1998. In a nutshell, a quantum vertex algebra is a braided state-field correspondence which 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.

arXiv comment32 pages

References in corpus (5)

• Field Algebras
• Finite vs. affine W-algebras
• On quantum vertex algebras and their modules
• Center of the quantum affine vertex algebra in type A
• $h$-adic quantum vertex algebras associated with rational $R$-matrix in types $B$, $C$ and $D$

Cited by in corpus (8)

• On the quantum affine vertex algebra associated with trigonometric $R$-matrix
• $h$-adic quantum vertex algebras in types $B$, $C$, $D$ and their $\varphi$-coordinated modules
• Logarithmic Vertex Algebras
• An approach to Quantum Conformal Algebra
• Yangian deformations of $\mathcal{S}$-commutative quantum vertex algebras and Bethe subalgebras
• On the $h$-adic quantum vertex algebras associated with Hecke symmetries
• On two families of quantum vertex algebras of FRT-type
• On the Heisenberg algebra associated with the rational $R$-matrix