Representations and identities of plactic-like monoids

Detalhes bibliográficos
Autor(a) principal: Cain, Alan J.
Data de Publicação: 2022
Outros Autores: Johnson, Marianne, Kambites, Mark, Malheiro, António
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/145310
Resumo: Publisher Copyright: © 2022
id RCAP_0e69eeb66033917c1578d45aa82fb82f
oai_identifier_str oai:run.unl.pt:10362/145310
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Representations and identities of plactic-like monoidsBaxter monoidHypoplactic monoidPlactic monoidRepresentationSemigroup identityStalactic monoidSylvester monoidTaiga monoidTropical semiringUpper triangular matrix semigroupVarietiesAlgebra and Number TheoryPublisher Copyright: © 2022We exhibit faithful representations of the hypoplactic, stalactic, taiga, sylvester, Baxter and right patience sorting monoids of each finite rank as monoids of upper triangular matrices over any semiring from a large class including the tropical semiring and fields of characteristic 0. By analysing the image of these representations, we show that the variety generated by a single hypoplactic (respectively, stalactic or taiga) monoid of rank at least 2 coincides with the variety generated by the natural numbers together with a fixed finite monoid H (respectively, F) and forms a proper subvariety of the variety generated by the plactic monoid of rank 2.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNCain, Alan J.Johnson, MarianneKambites, MarkMalheiro, António2022-11-08T22:13:31Z2022-09-152022-09-15T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article32application/pdfhttp://hdl.handle.net/10362/145310eng0021-8693PURE: 44857312https://doi.org/10.1016/j.jalgebra.2022.04.033info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T05:25:33Zoai:run.unl.pt:10362/145310Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:52:00.325807Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Representations and identities of plactic-like monoids
title Representations and identities of plactic-like monoids
spellingShingle Representations and identities of plactic-like monoids
Cain, Alan J.
Baxter monoid
Hypoplactic monoid
Plactic monoid
Representation
Semigroup identity
Stalactic monoid
Sylvester monoid
Taiga monoid
Tropical semiring
Upper triangular matrix semigroup
Varieties
Algebra and Number Theory
title_short Representations and identities of plactic-like monoids
title_full Representations and identities of plactic-like monoids
title_fullStr Representations and identities of plactic-like monoids
title_full_unstemmed Representations and identities of plactic-like monoids
title_sort Representations and identities of plactic-like monoids
author Cain, Alan J.
author_facet Cain, Alan J.
Johnson, Marianne
Kambites, Mark
Malheiro, António
author_role author
author2 Johnson, Marianne
Kambites, Mark
Malheiro, António
author2_role author
author
author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Cain, Alan J.
Johnson, Marianne
Kambites, Mark
Malheiro, António
dc.subject.por.fl_str_mv Baxter monoid
Hypoplactic monoid
Plactic monoid
Representation
Semigroup identity
Stalactic monoid
Sylvester monoid
Taiga monoid
Tropical semiring
Upper triangular matrix semigroup
Varieties
Algebra and Number Theory
topic Baxter monoid
Hypoplactic monoid
Plactic monoid
Representation
Semigroup identity
Stalactic monoid
Sylvester monoid
Taiga monoid
Tropical semiring
Upper triangular matrix semigroup
Varieties
Algebra and Number Theory
description Publisher Copyright: © 2022
publishDate 2022
dc.date.none.fl_str_mv 2022-11-08T22:13:31Z
2022-09-15
2022-09-15T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/145310
url http://hdl.handle.net/10362/145310
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0021-8693
PURE: 44857312
https://doi.org/10.1016/j.jalgebra.2022.04.033
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 32
application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
_version_ 1799138112326074368

Registros relacionados