Representation theory over local rings
Lead Research Organisation:
University of Manchester
Department Name: Mathematics
Abstract
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Organisations
People |
ORCID iD |
| Charles Eaton (Principal Investigator) |
Publications
Livesey M
(2019)
On Picard groups of blocks with normal defect groups
Linckelmann M
(2020)
Linear source invertible bimodules and Green correspondence
Livesey M
(2021)
Arbitrarily large O -Morita Frobenius numbers
in Journal of Algebra
Livesey M
(2021)
On Picent for blocks with normal defect group
in Journal of Algebra
Livesey M
(2021)
On Picard groups of blocks with normal defect groups
in Journal of Algebra
Linckelman M
(2021)
Linear source invertible bimodules and Green correspondence
in Journal of Pure and Applied Algebra
Eaton C
(2021)
Donovan's conjecture and extensions by the centralizer of a defect group
in Journal of Algebra
Livesey M
(2022)
Picard groups for blocks with normal defect groups and linear source bimodules
in Journal of Algebra
Eisele F
(2022)
Arbitrarily large Morita Frobenius numbers
in Algebra & Number Theory
Serwene P
(2023)
Proving a conjecture for fusion systems on a class of groups
Eaton C
(2024)
Morita equivalence classes of 2-blocks with abelian defect groups of rank 4
in Journal of the London Mathematical Society
Eisele F
(2024)
Units in blocks of defect 1 and the Zassenhaus conjecture
in Revista Matemática Complutense
Serwene P
(2024)
Proving a conjecture for fusion systems on a class of groups
in Journal of Algebra
Eaton C
(2025)
Blocks whose defect groups are Suzuki 2-groups
in Journal of Algebra
| Description | A large part of the project concerns Picard groups for blocks of finite groups. In recent research, these have been crucial in classifying blocks of finite groups up to Morita equivalence, however relatively little was known about them. For instance, they had only been calculated in restricted cases. In work by Livesey, Eaton and Livesey and Livesey and Marchi, Picard groups are determined in a wide range of cases, giving a foundation for further study. This further study includes work by Livesey and Linckelmann on bounding the size of certain important subgroups of the Picard group. |
| Exploitation Route | A foundation of cases in which the Picard group is known provides the means for further research on this emerging theme of study. |
| Sectors | Creative Economy |