Group conditional expectations of finite index

Open AccessOther

Group conditional expectations of finite index

Esteban Andruchow,Demetrio Stojanoff-1998-01-01-CERN Document Server (European Organization for Nuclear Research)

TL;DRAbstract

Let M be a von Neumann algebra with finite dimensional center, G a subgroup of the group of automorphisms of M such that M is G-finite and E : M → MG = {x ∈ M : g(x) = x for all g ∈ G} a faithful normal conditional expectation. Then E has finite index if and only if the group G has compact closure in B(M). The same result and its natural dinamical systems versions are proved for simple C∗-algebras.

Chat with Paper

AI Agents for this Paper

Let M be a von Neumann algebra with finite dimensional center, G a subgroup of the group of automorphisms of M such that M is G-finite and E : M → MG = {x ∈ M : g(x) = x for all g ∈ G} a faithful normal conditional expectation. Then E has finite index if and only if the group G has compact closure in B(M). The same result and its natural dinamical systems versions are proved for simple C∗-algebras.

Keywords

MathematicsAutomorphismGroup (periodic table)Finite groupCenter (category theory)Closure (psychology)Conditional expectationCombinatorics

Chat

Click to start Chat