On quantum groups associated to a pair of preregular forms

Alexandru Chirvasitu, Chelsea Walton, Xingting Wang

Research output: Contribution to journalArticlepeer-review


We define the universal quantum group H that preserves a pair of Hopf comodule maps, whose underlying vector space maps are preregular forms defined on dual vector spaces. This generalizes the construction of Bichon and Dubois-Violette (2013), where the target of these comodule maps are the ground field. We also recover the quantum groups introduced by Dubois-Violette and Launer (1990), by Takeuchi (1990), by Artin, Schelter, and Tate (1991), and by Mrozinski (2014), via our construction. As a consequence, we obtain an explicit presentation of a universal quantum group that coacts simultaneously on a pair of N-Koszul Artin–Schelter regular algebras with arbitrary quantum determinant.

Original languageEnglish (US)
Pages (from-to)115-159
Number of pages45
JournalJournal of Noncommutative Geometry
Issue number1
StatePublished - 2019


  • Artin–Schelter regular
  • Homological codeterminant
  • N-Koszul
  • Preregular form
  • Twisted superpotential
  • Universal quantum group

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Mathematical Physics
  • Geometry and Topology

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