Morita equivalence classes of blocks with elementary abelian defect groups of order 32

Cesare Giulio Ardito

doi:10.1016/j.jalgebra.2020.12.036

Morita equivalence classes of blocks with elementary abelian defect groups of order 32

Cesare Giulio Ardito

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We describe a general technique to classify blocks of finite groups, and we apply it to determine Morita equivalence classes of blocks with elementary abelian defect groups of order 32 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two. As a consequence we verify that a conjecture of Harada holds on these blocks.

Original language	English
Pages (from-to)	297-335
Number of pages	39
Journal	Journal of Algebra
Volume	573
Early online date	15 Jan 2021
DOIs	https://doi.org/10.1016/j.jalgebra.2020.12.036
Publication status	Published - 1 May 2021

Keywords

Block theory
Donovan's conjecture
Finite groups
Modular representation theory
Morita equivalence

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10.1016/j.jalgebra.2020.12.036

https://arxiv.org/pdf/1908.02652.pdf

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title = "Morita equivalence classes of blocks with elementary abelian defect groups of order 32",

abstract = "We describe a general technique to classify blocks of finite groups, and we apply it to determine Morita equivalence classes of blocks with elementary abelian defect groups of order 32 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two. As a consequence we verify that a conjecture of Harada holds on these blocks.",

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author = "Ardito, {Cesare Giulio}",

note = "Funding Information: This paper is part of the work done by the author during his PhD at the University of Manchester, supported by a Manchester Research Scholar Award and a University of Manchester President's Doctoral Scholar Award . Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",

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N2 - We describe a general technique to classify blocks of finite groups, and we apply it to determine Morita equivalence classes of blocks with elementary abelian defect groups of order 32 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two. As a consequence we verify that a conjecture of Harada holds on these blocks.

AB - We describe a general technique to classify blocks of finite groups, and we apply it to determine Morita equivalence classes of blocks with elementary abelian defect groups of order 32 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two. As a consequence we verify that a conjecture of Harada holds on these blocks.

KW - Block theory

KW - Donovan's conjecture

KW - Finite groups

KW - Modular representation theory

KW - Morita equivalence

U2 - 10.1016/j.jalgebra.2020.12.036

DO - 10.1016/j.jalgebra.2020.12.036

M3 - Article

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SN - 0021-8693

VL - 573

SP - 297

EP - 335

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Morita equivalence classes of blocks with elementary abelian defect groups of order 32

Abstract

Keywords

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