Quantum vertex algebras and their phi-coordinated quasi modules

Details Quantum vertex algebras and their phi-coordinated quasi modules Quantum vertex algebras and their phi-coordinated quasi modules

2009-06-15

arxiv.org/abs/0906.2710v2

Mathematics

Quantum Algebra

42 pages; extensively revised

Scientific paper

We develop a theory of $\phi$-coordinated (quasi) modules for a nonlocal vertex algebra and we establish a conceptual construction of nonlocal vertex algebras and their $\phi$-coordinated (quasi) modules, where $\phi$ is what we call an associate of the one-dimensional additive formal group. By specializing $\phi$ 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 $\phi$-coordinated modules to a certain quantum $\beta\gamma$-system.

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