Vol. 15, No. 4, 2021

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A proof of the Brown–Goodearl conjecture for module-finite weak Hopf algebras

Daniel Rogalski, Robert Won and James J. Zhang

Vol. 15 (2021), No. 4, 971–997
Abstract

Let H be a weak Hopf algebra that is a finitely generated module over its affine center. We show that H has finite self-injective dimension and so the Brown–Goodearl conjecture holds in this special weak Hopf setting.

Keywords
weak Hopf algebras, injective dimension, Brown–Goodearl conjecture
Mathematical Subject Classification 2010
Primary: 16E10
Secondary: 16T99, 18D10
Milestones
Received: 5 January 2020
Revised: 19 June 2020
Accepted: 11 October 2020
Published: 29 May 2021
Authors
Daniel Rogalski
Department of Mathematics
University of California, San Diego
La Jolla, CA
United States
Robert Won
Department of Mathematics
George Washington University
Washington, DC
United States
James J. Zhang
Department of Mathematics
University of Washington
Seattle, WA
United States