Primitive ideals of U-q(Sl(n)(+))
Autor(a) principal: | |
---|---|
Data de Publicação: | 2006 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/10216/126949 |
Resumo: | Let U-q(g(+)) be the quantized enveloping algebra of the nilpotent Lie algebra g(+) = sl(n+1)(+) which occurs as the positive part in the triangular decomposition of the simple Lie algebra sl(n+1) of type A(n). Assuming the base field K is algebraically closed and of characteristic 0, and that the parameter q is an element of K* is not a root of unity, we define and study certain quotients of U-q(g(+)) which coincide with the Weyl-Hayashi algebra when n = 2 (see Alev and Dumas, 1996, Hayashi, 1990; Kirkman and Small, 1993). We show that these are simple Noetherian domains, with a trivial center and even Gelfand-Kirillov dimension. Hence, they play a role analogous to that played by the Weyl algebras in the classical case. In the remainder of the article, we study the primitive spectrum of U-q(sl(4)(+)) in detail, somewhat in the spirit of Launois (to appear). We determine all primitive ideals of U-q(sl(4)(+)), find a set of generators for each one, compute their heights and find a simple U-q(sl(4)(+))-module corresponding to each primitive ideal of U-q(sl(4)(+)). |
id |
RCAP_0cc081ebb342e86de15ee4978a8ccfe4 |
---|---|
oai_identifier_str |
oai:repositorio-aberto.up.pt:10216/126949 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Primitive ideals of U-q(Sl(n)(+))MatemáticaMathematicsLet U-q(g(+)) be the quantized enveloping algebra of the nilpotent Lie algebra g(+) = sl(n+1)(+) which occurs as the positive part in the triangular decomposition of the simple Lie algebra sl(n+1) of type A(n). Assuming the base field K is algebraically closed and of characteristic 0, and that the parameter q is an element of K* is not a root of unity, we define and study certain quotients of U-q(g(+)) which coincide with the Weyl-Hayashi algebra when n = 2 (see Alev and Dumas, 1996, Hayashi, 1990; Kirkman and Small, 1993). We show that these are simple Noetherian domains, with a trivial center and even Gelfand-Kirillov dimension. Hence, they play a role analogous to that played by the Weyl algebras in the classical case. In the remainder of the article, we study the primitive spectrum of U-q(sl(4)(+)) in detail, somewhat in the spirit of Launois (to appear). We determine all primitive ideals of U-q(sl(4)(+)), find a set of generators for each one, compute their heights and find a simple U-q(sl(4)(+))-module corresponding to each primitive ideal of U-q(sl(4)(+)).20062006-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10216/126949eng0092-787210.1080/0927870600936682Samuel A Lopesinfo: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:RCAAP2023-11-29T15:03:12Zoai:repositorio-aberto.up.pt:10216/126949Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:14:31.706760Repositório 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 |
Primitive ideals of U-q(Sl(n)(+)) |
title |
Primitive ideals of U-q(Sl(n)(+)) |
spellingShingle |
Primitive ideals of U-q(Sl(n)(+)) Samuel A Lopes Matemática Mathematics |
title_short |
Primitive ideals of U-q(Sl(n)(+)) |
title_full |
Primitive ideals of U-q(Sl(n)(+)) |
title_fullStr |
Primitive ideals of U-q(Sl(n)(+)) |
title_full_unstemmed |
Primitive ideals of U-q(Sl(n)(+)) |
title_sort |
Primitive ideals of U-q(Sl(n)(+)) |
author |
Samuel A Lopes |
author_facet |
Samuel A Lopes |
author_role |
author |
dc.contributor.author.fl_str_mv |
Samuel A Lopes |
dc.subject.por.fl_str_mv |
Matemática Mathematics |
topic |
Matemática Mathematics |
description |
Let U-q(g(+)) be the quantized enveloping algebra of the nilpotent Lie algebra g(+) = sl(n+1)(+) which occurs as the positive part in the triangular decomposition of the simple Lie algebra sl(n+1) of type A(n). Assuming the base field K is algebraically closed and of characteristic 0, and that the parameter q is an element of K* is not a root of unity, we define and study certain quotients of U-q(g(+)) which coincide with the Weyl-Hayashi algebra when n = 2 (see Alev and Dumas, 1996, Hayashi, 1990; Kirkman and Small, 1993). We show that these are simple Noetherian domains, with a trivial center and even Gelfand-Kirillov dimension. Hence, they play a role analogous to that played by the Weyl algebras in the classical case. In the remainder of the article, we study the primitive spectrum of U-q(sl(4)(+)) in detail, somewhat in the spirit of Launois (to appear). We determine all primitive ideals of U-q(sl(4)(+)), find a set of generators for each one, compute their heights and find a simple U-q(sl(4)(+))-module corresponding to each primitive ideal of U-q(sl(4)(+)). |
publishDate |
2006 |
dc.date.none.fl_str_mv |
2006 2006-01-01T00:00:00Z |
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 |
https://hdl.handle.net/10216/126949 |
url |
https://hdl.handle.net/10216/126949 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0092-7872 10.1080/0927870600936682 |
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: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_ |
1799136066274328576 |