Arbitrarily large Morita Frobenius numbers

Eisele, Florian; Livesey, Michael

doi:10.2140/ant.2022.16.1889

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Arbitrarily large Morita Frobenius numbers

Florian Eisele and Michael Livesey

Vol. 16 (2022), No. 8, 1889–1904

DOI: 10.2140/ant.2022.16.1889

Abstract

We construct blocks of finite groups with arbitrarily large Morita Frobenius numbers, an invariant which determines the size of the minimal field of definition of the associated basic algebra. This answers a question of Benson and Kessar. This also improves upon a result of the second author where arbitrarily large $𝒪$ -Morita Frobenius numbers are constructed.

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Keywords

modular representation theory, block theory, Morita Frobenius numbers

Mathematical Subject Classification

Primary: 20C20

Milestones

Received: 23 July 2020

Revised: 17 August 2021

Accepted: 24 December 2021

Published: 29 November 2022

Authors

Florian Eisele
Department of Mathematics University of Manchester Manchester United Kingdom

Michael Livesey
Department of Mathematics University of Manchester Manchester United Kingdom

Vol. 16, No. 8, 2022