Constructing quantum vertex algebras

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This is a sequel to [23], In this paper, we focus on the construction of quantum vertex algebras over ℂ whose notion was formulated in [23] with Etingof and Kazhdan's notion of quantum vertex operator algebra (over ℂ[[h]]) as one of the main motivations. As one of the main steps in constructing quantum vertex algebras, we prove that every countable-dimensional nonlocal (namely, noncommutative) vertex algebra over ℂ, which either is irreducible or has a basis of PBW type, is nondegenerate in the sense of Etingof and Kazhdan. Using this result, we establish the nondegeneracy of better known vertex operator algebras and some newly constructed nonlocal vertex algebras. We construct a family of quantum vertex algebras closely related to Zamolodchikov-Faddeev algebras.

Original languageEnglish (US)
Pages (from-to)441-476
Number of pages36
JournalInternational Journal of Mathematics
Issue number4
StatePublished - Apr 2006

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • Nondegeneracy
  • Nonlocal vertex algebra
  • Quantum vertex algebra

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