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Arbitrarily large Morita Frobenius numbers

Florian Eisele and Michael Livesey

Vol. 16 (2022), No. 8, 1889–1904
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.

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