The Weyl group and the normalizer of a conditional expectation
- Autores
- Argerami, Martín; Stojanoff, Demetrio
- Año de publicación
- 1999
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We define a discrete group W(E) associated to a faithful normal conditional expectation E : M → N for N ⊆ M von Neuman algebras. This group shows the relation between the unitary group UN and the normalizer NE of E, which can be also considered as the isotropy of the action of the unitary group UM of M on E. It is shown that W(E) is finite if dim Z(N) < ∞ and bounded by the index in the factor case. Also sharp bounds of the order of W(E) are founded. W(E) appears as the fibre of a covering space defined on the orbit of E by the natural action of the unitary group of M. W(E) is computed in some basic examples.
Facultad de Ciencias Exactas - Materia
-
Ciencias Exactas
Matemática
Física
Weyl group
Algebra
Normalizer
Conditional expectation - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc-sa/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/123300
Ver los metadatos del registro completo
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The Weyl group and the normalizer of a conditional expectationArgerami, MartínStojanoff, DemetrioCiencias ExactasMatemáticaFísicaWeyl groupAlgebraNormalizerConditional expectationWe define a discrete group W(E) associated to a faithful normal conditional expectation E : M → N for N ⊆ M von Neuman algebras. This group shows the relation between the unitary group U<sub>N</sub> and the normalizer N<sub>E</sub> of E, which can be also considered as the isotropy of the action of the unitary group U<sub>M</sub> of M on E. It is shown that W(E) is finite if dim Z(N) < ∞ and bounded by the index in the factor case. Also sharp bounds of the order of W(E) are founded. W(E) appears as the fibre of a covering space defined on the orbit of E by the natural action of the unitary group of M. W(E) is computed in some basic examples.Facultad de Ciencias Exactas1999info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf165-186http://sedici.unlp.edu.ar/handle/10915/123300enginfo:eu-repo/semantics/altIdentifier/issn/0378-620Xinfo:eu-repo/semantics/altIdentifier/issn/1420-8989info:eu-repo/semantics/altIdentifier/doi/10.1007/bf01236470info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-03T11:01:22Zoai:sedici.unlp.edu.ar:10915/123300Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-03 11:01:22.861SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| dc.title.none.fl_str_mv |
The Weyl group and the normalizer of a conditional expectation |
| title |
The Weyl group and the normalizer of a conditional expectation |
| spellingShingle |
The Weyl group and the normalizer of a conditional expectation Argerami, Martín Ciencias Exactas Matemática Física Weyl group Algebra Normalizer Conditional expectation |
| title_short |
The Weyl group and the normalizer of a conditional expectation |
| title_full |
The Weyl group and the normalizer of a conditional expectation |
| title_fullStr |
The Weyl group and the normalizer of a conditional expectation |
| title_full_unstemmed |
The Weyl group and the normalizer of a conditional expectation |
| title_sort |
The Weyl group and the normalizer of a conditional expectation |
| dc.creator.none.fl_str_mv |
Argerami, Martín Stojanoff, Demetrio |
| author |
Argerami, Martín |
| author_facet |
Argerami, Martín Stojanoff, Demetrio |
| author_role |
author |
| author2 |
Stojanoff, Demetrio |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
Ciencias Exactas Matemática Física Weyl group Algebra Normalizer Conditional expectation |
| topic |
Ciencias Exactas Matemática Física Weyl group Algebra Normalizer Conditional expectation |
| dc.description.none.fl_txt_mv |
We define a discrete group W(E) associated to a faithful normal conditional expectation E : M → N for N ⊆ M von Neuman algebras. This group shows the relation between the unitary group U<sub>N</sub> and the normalizer N<sub>E</sub> of E, which can be also considered as the isotropy of the action of the unitary group U<sub>M</sub> of M on E. It is shown that W(E) is finite if dim Z(N) < ∞ and bounded by the index in the factor case. Also sharp bounds of the order of W(E) are founded. W(E) appears as the fibre of a covering space defined on the orbit of E by the natural action of the unitary group of M. W(E) is computed in some basic examples. Facultad de Ciencias Exactas |
| description |
We define a discrete group W(E) associated to a faithful normal conditional expectation E : M → N for N ⊆ M von Neuman algebras. This group shows the relation between the unitary group U<sub>N</sub> and the normalizer N<sub>E</sub> of E, which can be also considered as the isotropy of the action of the unitary group U<sub>M</sub> of M on E. It is shown that W(E) is finite if dim Z(N) < ∞ and bounded by the index in the factor case. Also sharp bounds of the order of W(E) are founded. W(E) appears as the fibre of a covering space defined on the orbit of E by the natural action of the unitary group of M. W(E) is computed in some basic examples. |
| publishDate |
1999 |
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1999 |
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