JournalsjncgVol. 18, No. 4pp. 1453–1483

A cogroupoid associated to preregular forms

  • Hongdi Huang

    Rice University, Houston, USA

  • Van C. Nguyen

    United States Naval Academy, Annapolis, USA

  • Charlotte Ure

    Illinois State University, Normal, USA

  • Kent B. Vashaw

    Massachusetts Institute of Technology, Cambridge, USA

  • Padmini Veerapen

    Tennessee Tech University, Cookeville, USA

  • Xingting Wang

    Louisiana State University, Baton Rouge, USA
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Abstract

We construct a family of cogroupoids associated to preregular forms and recover the Morita–Takeuchi equivalence for Artin–Schelter regular algebras of dimension two, observed by Raedschelders and Van den Bergh. Moreover, we study the 2-cocycle twists of pivotal analogues of these cogroupoids, by developing a categorical description of preregularity in any tensor category that has a pivotal structure.

Cite this article

Hongdi Huang, Van C. Nguyen, Charlotte Ure, Kent B. Vashaw, Padmini Veerapen, Xingting Wang, A cogroupoid associated to preregular forms. J. Noncommut. Geom. 18 (2024), no. 4, pp. 1453–1483

DOI 10.4171/JNCG/558