A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMS
Autor(a) principal: | |
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Data de Publicação: | 2015 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://hdl.handle.net/10216/111068 |
Resumo: | An Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra A(h) generated by elements x, y, which satisfy yx - xy = h, where h is an element of F[x]. We investigate the family of algebras A(h) as h ranges over all the polynomials in F[x]. When h not equal 0, the algebras A(h) are subalgebras of the Weyl algebra A(1) and can be viewed as differential operators with polynomial coefficients. We give an exact description of the automorphisms of A(h) over arbitrary fields F and describe the invariants in A(h) under the automorphisms. We determine the center, normal elements, and height one prime ideals of A(h), localizations and Ore sets for A(h), and the Lie ideal [A(h), A(h)]. We also show that A(h) cannot be realized as a generalized Weyl algebra over F[x], except when h is an element of F. In two sequels to this work, we completely describe the irreducible modules and derivations of A(h) over any field. |
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A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMSMatemáticaMathematicsAn Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra A(h) generated by elements x, y, which satisfy yx - xy = h, where h is an element of F[x]. We investigate the family of algebras A(h) as h ranges over all the polynomials in F[x]. When h not equal 0, the algebras A(h) are subalgebras of the Weyl algebra A(1) and can be viewed as differential operators with polynomial coefficients. We give an exact description of the automorphisms of A(h) over arbitrary fields F and describe the invariants in A(h) under the automorphisms. We determine the center, normal elements, and height one prime ideals of A(h), localizations and Ore sets for A(h), and the Lie ideal [A(h), A(h)]. We also show that A(h) cannot be realized as a generalized Weyl algebra over F[x], except when h is an element of F. In two sequels to this work, we completely describe the irreducible modules and derivations of A(h) over any field.20152015-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/10216/111068eng0002-994710.1090/conm/602/12027Georgia BenkartSamuel A LopesMatthew Ondrusinfo: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:RCAAP2023-11-29T16:15:01Zoai:repositorio-aberto.up.pt:10216/111068Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:39:52.016084Repositório 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 |
A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMS |
title |
A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMS |
spellingShingle |
A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMS Georgia Benkart Matemática Mathematics |
title_short |
A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMS |
title_full |
A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMS |
title_fullStr |
A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMS |
title_full_unstemmed |
A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMS |
title_sort |
A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMS |
author |
Georgia Benkart |
author_facet |
Georgia Benkart Samuel A Lopes Matthew Ondrus |
author_role |
author |
author2 |
Samuel A Lopes Matthew Ondrus |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Georgia Benkart Samuel A Lopes Matthew Ondrus |
dc.subject.por.fl_str_mv |
Matemática Mathematics |
topic |
Matemática Mathematics |
description |
An Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra A(h) generated by elements x, y, which satisfy yx - xy = h, where h is an element of F[x]. We investigate the family of algebras A(h) as h ranges over all the polynomials in F[x]. When h not equal 0, the algebras A(h) are subalgebras of the Weyl algebra A(1) and can be viewed as differential operators with polynomial coefficients. We give an exact description of the automorphisms of A(h) over arbitrary fields F and describe the invariants in A(h) under the automorphisms. We determine the center, normal elements, and height one prime ideals of A(h), localizations and Ore sets for A(h), and the Lie ideal [A(h), A(h)]. We also show that A(h) cannot be realized as a generalized Weyl algebra over F[x], except when h is an element of F. In two sequels to this work, we completely describe the irreducible modules and derivations of A(h) over any field. |
publishDate |
2015 |
dc.date.none.fl_str_mv |
2015 2015-01-01T00:00:00Z |
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/10216/111068 |
url |
https://hdl.handle.net/10216/111068 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0002-9947 10.1090/conm/602/12027 |
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 |
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1799136305175592960 |