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

Daniel Rogalski; Robert Won; James J. Zhang

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.

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Daniel Rogalski. Robert Won. James J. Zhang. "A proof of the Brown–Goodearl conjecture for module-finite weak Hopf algebras." Algebra Number Theory 15 (4) 971 - 997, 2021. https://doi.org/10.2140/ant.2021.15.971

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Received: 5 January 2020; Revised: 19 June 2020; Accepted: 11 October 2020; Published: 2021

First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.2140/ant.2021.15.971

Subjects:

Primary: 16E10

Secondary: 16T99 , 18D10

Keywords: Brown–Goodearl conjecture , injective dimension , weak Hopf algebras

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