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

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

2009-03-01

arxiv.org/abs/0903.0186v2

Mathematics

Quantum Algebra

47 pages, extensively revised

Scientific paper

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.

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