On quantum groups associated to a pair of preregular forms

  • Alexandru Chirvasitu

    University of Washington, Seattle, USA
  • Chelsea Walton

    Temple University, Philadelphia, USA
  • Xingting Wang

    Temple University, Philadelphia, USA
On quantum groups associated to a pair of preregular forms cover
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Abstract

We define the universal quantum group 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.

Cite this article

Alexandru Chirvasitu, Chelsea Walton, Xingting Wang, On quantum groups associated to a pair of preregular forms. J. Noncommut. Geom. 13 (2019), no. 1, pp. 115–159

DOI 10.4171/JNCG/306