Quantum vertex algebras and their phi-coordinated quasi modules

Abstract

We develop a theory of $\varphi$-coordinated (quasi) modules for a nonlocal vertex algebra and we establish a conceptual construction of nonlocal vertex algebras and their $\varphi$-coordinated (quasi) modules, where $\varphi$ is what we call an associate of the one-dimensional additive formal group. By specializing $\varphi$ to a particular associate, we obtain a new construction of weak quantum vertex algebras in the sense of \cite{li-qva1}. As an application, we associate weak quantum vertex algebras to quantum affine algebras, and we also associate quantum vertex algebras and $\varphi$-coordinated modules to a certain quantum $\beta \gamma$-system.

42 pages; extensively revised

References in corpus (5)

• Field Algebras
• Constructing quantum vertex algebras
• On quantum vertex algebras and their modules
• $H_D$-Quantum Vertex Algebras and Bicharacters
• Quantum vertex $F((t))$-algebras and their modules

Cited by in corpus (2)

• Vertex operators and principal subspaces of level one for $U_q({\widehat{\mathfrak{sl}}}_2)$
• Associating quantum vertex algebras to certain deformed Heisenberg Lie algebras