Conjugacy classes of left ideals of a finite dimensional algebra

Let A be a finite dimensional unital algebra over a field K and let C(A) denote the set of conjugacy classes of left ideals in A. It is shown that C(A) is finite if and only if the number of conjugacy classes of nilpotent left ideals in A is finite. The set C(A) can be considered as a semigroup unde...

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Detalles Bibliográficos
Autores: Meçel, Arkadiusz, Okniński, Jan
Tipo de recurso: artículo
Fecha de publicación:2013
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:107341
Acceso en línea:https://ddd.uab.cat/record/107341
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_57213_10
Access Level:acceso abierto
Palabra clave:Finite dimensional algebra
Left ideal
Semigroup
Conjugacy class
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spelling Conjugacy classes of left ideals of a finite dimensional algebraMeçel, ArkadiuszOkniński, JanFinite dimensional algebraLeft idealSemigroupConjugacy classLet A be a finite dimensional unital algebra over a field K and let C(A) denote the set of conjugacy classes of left ideals in A. It is shown that C(A) is finite if and only if the number of conjugacy classes of nilpotent left ideals in A is finite. The set C(A) can be considered as a semigroup under the natural operation induced from the multiplication in A. If K is algebraically closed, the square of the radical of A is zero and C(A) is finite, then for every K-algebra B such that C(B) ≡ C(A) it is shown that B ≡ A. 22013-01-0120132013-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/107341https://dx.doi.org/urn:doi:10.5565/PUBLMAT_57213_10reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1073412026-06-06T12:50:31Z
dc.title.none.fl_str_mv Conjugacy classes of left ideals of a finite dimensional algebra
title Conjugacy classes of left ideals of a finite dimensional algebra
spellingShingle Conjugacy classes of left ideals of a finite dimensional algebra
Meçel, Arkadiusz
Finite dimensional algebra
Left ideal
Semigroup
Conjugacy class
title_short Conjugacy classes of left ideals of a finite dimensional algebra
title_full Conjugacy classes of left ideals of a finite dimensional algebra
title_fullStr Conjugacy classes of left ideals of a finite dimensional algebra
title_full_unstemmed Conjugacy classes of left ideals of a finite dimensional algebra
title_sort Conjugacy classes of left ideals of a finite dimensional algebra
dc.creator.none.fl_str_mv Meçel, Arkadiusz
Okniński, Jan
author Meçel, Arkadiusz
author_facet Meçel, Arkadiusz
Okniński, Jan
author_role author
author2 Okniński, Jan
author2_role author
dc.subject.none.fl_str_mv Finite dimensional algebra
Left ideal
Semigroup
Conjugacy class
topic Finite dimensional algebra
Left ideal
Semigroup
Conjugacy class
description Let A be a finite dimensional unital algebra over a field K and let C(A) denote the set of conjugacy classes of left ideals in A. It is shown that C(A) is finite if and only if the number of conjugacy classes of nilpotent left ideals in A is finite. The set C(A) can be considered as a semigroup under the natural operation induced from the multiplication in A. If K is algebraically closed, the square of the radical of A is zero and C(A) is finite, then for every K-algebra B such that C(B) ≡ C(A) it is shown that B ≡ A.
publishDate 2013
dc.date.none.fl_str_mv 2
2013-01-01
2013
2013-01-01
dc.type.none.fl_str_mv Article
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url https://ddd.uab.cat/record/107341
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_57213_10
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
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