On irreducible infinite conformal algebras
- Autores
- Boyallian, Carina; Liberati, Jose Ignacio
- Año de publicación
- 2004
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- The associative conformal algebra CendN and the corresponding general Lie conformal algebra gcN are the most important examples of simple conformal algebras which are not finite (see Sect. 2.10 in [K1]). One of the most important open problems of the theory of conformal algebras is the classification of infinite subalgebras of CendN and of gcN which act irreducibly on C[∂] N . (For a classification of such finite algebras, in the associative case see Theorem 2.6 of the present paper, and in the (more difficult) Lie case see [CK] and [DK].) The classical Burnside theorem states that any subalgebra of the matrix algebra MatN C that acts irreducibly on C N is the whole algebra MatN C. This is certainly not true for subalgebras of CendN (which is the “conformal” analogue of MatN C). There is a family of infinite subalgebras CendN,P of CendN , where P(x) ∈ MatN C[x], det P(x) 6= 0, that still act irreducibly on C[∂] N . One of the conjectures of [K2] states that there are no other infinite irreducible subalgebras of CendN . This conjecture was recently proved by Kolesnikov [Ko]. In the Lie conformal case, we have a conjecture on the classification of infinite Lie conformal subalgebras of gcN acting irreducibly on C[∂] N , see Conjecture 4.4. This conjecture agrees with recent results of E. Zelmanov [Z2] and A. De Sole - V. Kac.
Fil: Boyallian, Carina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Fil: Liberati, Jose Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina - Materia
-
ALGEBRAS
IRREDUCIBLE INFINITE - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/230890
Ver los metadatos del registro completo
| id |
CONICETDig_0ddf350c839968ee0876b061f8f13eca |
|---|---|
| oai_identifier_str |
oai:ri.conicet.gov.ar:11336/230890 |
| network_acronym_str |
CONICETDig |
| repository_id_str |
3498 |
| network_name_str |
CONICET Digital (CONICET) |
| spelling |
On irreducible infinite conformal algebrasBoyallian, CarinaLiberati, Jose IgnacioALGEBRASIRREDUCIBLE INFINITEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The associative conformal algebra CendN and the corresponding general Lie conformal algebra gcN are the most important examples of simple conformal algebras which are not finite (see Sect. 2.10 in [K1]). One of the most important open problems of the theory of conformal algebras is the classification of infinite subalgebras of CendN and of gcN which act irreducibly on C[∂] N . (For a classification of such finite algebras, in the associative case see Theorem 2.6 of the present paper, and in the (more difficult) Lie case see [CK] and [DK].) The classical Burnside theorem states that any subalgebra of the matrix algebra MatN C that acts irreducibly on C N is the whole algebra MatN C. This is certainly not true for subalgebras of CendN (which is the “conformal” analogue of MatN C). There is a family of infinite subalgebras CendN,P of CendN , where P(x) ∈ MatN C[x], det P(x) 6= 0, that still act irreducibly on C[∂] N . One of the conjectures of [K2] states that there are no other infinite irreducible subalgebras of CendN . This conjecture was recently proved by Kolesnikov [Ko]. In the Lie conformal case, we have a conjecture on the classification of infinite Lie conformal subalgebras of gcN acting irreducibly on C[∂] N , see Conjecture 4.4. This conjecture agrees with recent results of E. Zelmanov [Z2] and A. De Sole - V. Kac.Fil: Boyallian, Carina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Liberati, Jose Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaUniversidade de São Paulo2004-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/230890Boyallian, Carina; Liberati, Jose Ignacio; On irreducible infinite conformal algebras; Universidade de São Paulo; Resenhas Do Instituto de Matematica E Estatistica Da Universidade de Sao Paulo; 6; 12-2004; 129-1400104-3854CONICET DigitalCONICETenginfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:17:01Zoai:ri.conicet.gov.ar:11336/230890instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-10 13:17:01.791CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
On irreducible infinite conformal algebras |
| title |
On irreducible infinite conformal algebras |
| spellingShingle |
On irreducible infinite conformal algebras Boyallian, Carina ALGEBRAS IRREDUCIBLE INFINITE |
| title_short |
On irreducible infinite conformal algebras |
| title_full |
On irreducible infinite conformal algebras |
| title_fullStr |
On irreducible infinite conformal algebras |
| title_full_unstemmed |
On irreducible infinite conformal algebras |
| title_sort |
On irreducible infinite conformal algebras |
| dc.creator.none.fl_str_mv |
Boyallian, Carina Liberati, Jose Ignacio |
| author |
Boyallian, Carina |
| author_facet |
Boyallian, Carina Liberati, Jose Ignacio |
| author_role |
author |
| author2 |
Liberati, Jose Ignacio |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
ALGEBRAS IRREDUCIBLE INFINITE |
| topic |
ALGEBRAS IRREDUCIBLE INFINITE |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
The associative conformal algebra CendN and the corresponding general Lie conformal algebra gcN are the most important examples of simple conformal algebras which are not finite (see Sect. 2.10 in [K1]). One of the most important open problems of the theory of conformal algebras is the classification of infinite subalgebras of CendN and of gcN which act irreducibly on C[∂] N . (For a classification of such finite algebras, in the associative case see Theorem 2.6 of the present paper, and in the (more difficult) Lie case see [CK] and [DK].) The classical Burnside theorem states that any subalgebra of the matrix algebra MatN C that acts irreducibly on C N is the whole algebra MatN C. This is certainly not true for subalgebras of CendN (which is the “conformal” analogue of MatN C). There is a family of infinite subalgebras CendN,P of CendN , where P(x) ∈ MatN C[x], det P(x) 6= 0, that still act irreducibly on C[∂] N . One of the conjectures of [K2] states that there are no other infinite irreducible subalgebras of CendN . This conjecture was recently proved by Kolesnikov [Ko]. In the Lie conformal case, we have a conjecture on the classification of infinite Lie conformal subalgebras of gcN acting irreducibly on C[∂] N , see Conjecture 4.4. This conjecture agrees with recent results of E. Zelmanov [Z2] and A. De Sole - V. Kac. Fil: Boyallian, Carina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina Fil: Liberati, Jose Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina |
| description |
The associative conformal algebra CendN and the corresponding general Lie conformal algebra gcN are the most important examples of simple conformal algebras which are not finite (see Sect. 2.10 in [K1]). One of the most important open problems of the theory of conformal algebras is the classification of infinite subalgebras of CendN and of gcN which act irreducibly on C[∂] N . (For a classification of such finite algebras, in the associative case see Theorem 2.6 of the present paper, and in the (more difficult) Lie case see [CK] and [DK].) The classical Burnside theorem states that any subalgebra of the matrix algebra MatN C that acts irreducibly on C N is the whole algebra MatN C. This is certainly not true for subalgebras of CendN (which is the “conformal” analogue of MatN C). There is a family of infinite subalgebras CendN,P of CendN , where P(x) ∈ MatN C[x], det P(x) 6= 0, that still act irreducibly on C[∂] N . One of the conjectures of [K2] states that there are no other infinite irreducible subalgebras of CendN . This conjecture was recently proved by Kolesnikov [Ko]. In the Lie conformal case, we have a conjecture on the classification of infinite Lie conformal subalgebras of gcN acting irreducibly on C[∂] N , see Conjecture 4.4. This conjecture agrees with recent results of E. Zelmanov [Z2] and A. De Sole - V. Kac. |
| publishDate |
2004 |
| dc.date.none.fl_str_mv |
2004-12 |
| dc.type.none.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
| format |
article |
| status_str |
publishedVersion |
| dc.identifier.none.fl_str_mv |
http://hdl.handle.net/11336/230890 Boyallian, Carina; Liberati, Jose Ignacio; On irreducible infinite conformal algebras; Universidade de São Paulo; Resenhas Do Instituto de Matematica E Estatistica Da Universidade de Sao Paulo; 6; 12-2004; 129-140 0104-3854 CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/230890 |
| identifier_str_mv |
Boyallian, Carina; Liberati, Jose Ignacio; On irreducible infinite conformal algebras; Universidade de São Paulo; Resenhas Do Instituto de Matematica E Estatistica Da Universidade de Sao Paulo; 6; 12-2004; 129-140 0104-3854 CONICET Digital CONICET |
| dc.language.none.fl_str_mv |
eng |
| language |
eng |
| dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
| eu_rights_str_mv |
openAccess |
| rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
| dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
| dc.publisher.none.fl_str_mv |
Universidade de São Paulo |
| publisher.none.fl_str_mv |
Universidade de São Paulo |
| dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
| reponame_str |
CONICET Digital (CONICET) |
| collection |
CONICET Digital (CONICET) |
| instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
| repository.name.fl_str_mv |
CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
| repository.mail.fl_str_mv |
dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
| _version_ |
1842980930219671552 |
| score |
12.993085 |