The Weyl group and the normalizer of a conditional expectation
- Cite this article as:
- Argerami, M. & Stojanoff, D. Integr equ oper theory (1999) 34: 165. doi:10.1007/BF01236470
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We define a discrete groupW(E) associated to a faithful normal conditional expectationE : M → N forN ⊑M von Neuman algebras. This group shows the relation between the unitary groupUN and the normalizerNE ofE, which can be also considered as the isotropy of the action of the unitary groupUM ofM onE. It is shown thatW(E) is finite if dimZ(N)<∞ and bounded by the index in the factor case. Also sharp bounds of the order ofW(E) are founded.W(E) appears as the fibre of a covering space defined on the orbit ofE by the natural action of the unitary group ofM. W(E) is computed in some basic examples.