A Schur ring approach to supercharacters of adjoint groups and related subgroups

Bibliographic Details
Main Author: Silva, Tânia Sofia Zaragoza Cotrim
Publication Date: 2023
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10451/64830
Summary: Using the correspondence between central Schur rings and supercharacter theories for finite groups, we simplify the construction of the standard supercharacter theory for adjoint groups of finite radical rings. If the radical ring R is of odd characteristic and is endowed with an anti-involution σ, we define a supercharacter theory for the subgroup of the adjoint group R◦ , R◦ σ , consisting of elements fixed by σ. This theory extends the one previously defined in [9], when R is a nilpotent algebra over a finite field.
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spelling A Schur ring approach to supercharacters of adjoint groups and related subgroupsAnéis de SchurTeoria de SupercaracteresGrupo AdjuntoSchur ringsSupercharacter TheoryAdjoint GroupDomínio/Área Científica::Ciências Naturais::MatemáticasUsing the correspondence between central Schur rings and supercharacter theories for finite groups, we simplify the construction of the standard supercharacter theory for adjoint groups of finite radical rings. If the radical ring R is of odd characteristic and is endowed with an anti-involution σ, we define a supercharacter theory for the subgroup of the adjoint group R◦ , R◦ σ , consisting of elements fixed by σ. This theory extends the one previously defined in [9], when R is a nilpotent algebra over a finite field.André, Carlos Alberto MartinsFreitas, Pedro Jorge SantosRepositório da Universidade de LisboaSilva, Tânia Sofia Zaragoza Cotrim2024-05-24T09:56:03Z2023-122023-072023-12-01T00:00:00Zdoctoral thesisinfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10451/64830TID:101517505enginfo:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2025-03-17T15:15:47Zoai:repositorio.ulisboa.pt:10451/64830Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-29T03:38:11.599403Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv A Schur ring approach to supercharacters of adjoint groups and related subgroups
title A Schur ring approach to supercharacters of adjoint groups and related subgroups
spellingShingle A Schur ring approach to supercharacters of adjoint groups and related subgroups
Silva, Tânia Sofia Zaragoza Cotrim
Anéis de Schur
Teoria de Supercaracteres
Grupo Adjunto
Schur rings
Supercharacter Theory
Adjoint Group
Domínio/Área Científica::Ciências Naturais::Matemáticas
title_short A Schur ring approach to supercharacters of adjoint groups and related subgroups
title_full A Schur ring approach to supercharacters of adjoint groups and related subgroups
title_fullStr A Schur ring approach to supercharacters of adjoint groups and related subgroups
title_full_unstemmed A Schur ring approach to supercharacters of adjoint groups and related subgroups
title_sort A Schur ring approach to supercharacters of adjoint groups and related subgroups
author Silva, Tânia Sofia Zaragoza Cotrim
author_facet Silva, Tânia Sofia Zaragoza Cotrim
author_role author
dc.contributor.none.fl_str_mv André, Carlos Alberto Martins
Freitas, Pedro Jorge Santos
Repositório da Universidade de Lisboa
dc.contributor.author.fl_str_mv Silva, Tânia Sofia Zaragoza Cotrim
dc.subject.por.fl_str_mv Anéis de Schur
Teoria de Supercaracteres
Grupo Adjunto
Schur rings
Supercharacter Theory
Adjoint Group
Domínio/Área Científica::Ciências Naturais::Matemáticas
topic Anéis de Schur
Teoria de Supercaracteres
Grupo Adjunto
Schur rings
Supercharacter Theory
Adjoint Group
Domínio/Área Científica::Ciências Naturais::Matemáticas
description Using the correspondence between central Schur rings and supercharacter theories for finite groups, we simplify the construction of the standard supercharacter theory for adjoint groups of finite radical rings. If the radical ring R is of odd characteristic and is endowed with an anti-involution σ, we define a supercharacter theory for the subgroup of the adjoint group R◦ , R◦ σ , consisting of elements fixed by σ. This theory extends the one previously defined in [9], when R is a nilpotent algebra over a finite field.
publishDate 2023
dc.date.none.fl_str_mv 2023-12
2023-07
2023-12-01T00:00:00Z
2024-05-24T09:56:03Z
dc.type.driver.fl_str_mv doctoral thesis
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10451/64830
TID:101517505
url http://hdl.handle.net/10451/64830
identifier_str_mv TID:101517505
dc.language.iso.fl_str_mv eng
language eng
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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