A cogroupoid associated to preregular forms

Hongdi Huang; Van C. Nguyen; Charlotte Ure; Kent B. Vashaw; Padmini Veerapen; Xingting Wang

doi:10.4171/jncg/558

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

A cogroupoid associated to preregular forms

Hongdi Huang
Rice University, Houston, USA
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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