Abstract
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 groupU N and the normalizerN E ofE, which can be also considered as the isotropy of the action of the unitary groupU M 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.
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