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

Rogalski, Daniel; Won, Robert; Zhang, James J.

doi:10.2140/ant.2021.15.971

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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

DOI: 10.2140/ant.2021.15.971

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

Vol. 15, No. 4, 2021