Quantum vertex $F((t))$-algebras and their modules

Abstract

This is a paper in a series to study vertex algebra-like structures arising from various algebras including quantum affine algebras and Yangians. In this paper, we develop a theory of what we call (weak) quantum vertex $\F((t))$-algebras with $\F$ a field of characteristic zero and $t$ a formal variable, and we give a conceptual construction of (weak) quantum vertex $\F((t))$-algebras and their modules. As an application, we associate weak quantum vertex $\F((t))$-algebras to quantum affine algebras, providing a solution to a problem posed by Frenkel and Jing. We also explicitly construct an example of quantum vertex $\F((t))$-algebras from a certain quantum $\beta \gamma$-system.

47 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
• Nonlocal vertex algebras generated by formal vertex operators

Cited by in corpus (5)

• Vertex operators and principal subspaces of level one for $U_q({\widehat{\mathfrak{sl}}}_2)$
• A note on the zeroth products of Frenkel-Jing operators
• Quantum vertex algebras and their phi-coordinated quasi modules
• Quantum vertex $C((t))$-algebras and quantum affine algebras
• Vertex algebras associated with elliptic affine Lie algebras