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

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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 βγ-system.

Original languageEnglish (US)
Pages (from-to)2262-2304
Number of pages43
JournalJournal of Algebra
Volume324
Issue number9
DOIs
StatePublished - Nov 1 2010

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Nonlocal vertex algebra
  • Quantum Yang-Baxter operator
  • Quantum vertex algebra

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