HD-quantum vertex algebras and bicharacters

Iana I. Anguelova, Maarten J. Bergvelt

Research output: Contribution to journalArticlepeer-review


We define a new class of quantum vertex algebras, based on the Hopf algebra HD = [D] of "infinitesimal translations" generated by D. Besides the braiding map describing the obstruction to commutativity of products of vertex operators, HD-quantum vertex algebras have as a main new ingredient a "translation map" that describes the obstruction of vertex operators to satisfying translation covariance. The translation map also appears as obstruction to the state-field correspondence being a homomorphism. We use a bicharacter construction of Borcherds to construct a large class of HD-quantum vertex algebras. One particular example of this construction yields a quantum vertex algebra that contains the quantum vertex operators introduced by Jing in the theory of HallLittlewood polynomials.

Original languageEnglish (US)
Pages (from-to)937-991
Number of pages55
JournalCommunications in Contemporary Mathematics
Issue number6
StatePublished - Dec 2009


  • Bicharacter
  • Quantum vertex algebra

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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