The Weyl group and the normalizer of a conditional expectation
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 is...
Guardado en:
| Autores principales: | , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
1999
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/123300 |
| Aporte de: |
| Sumario: | 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. |
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