A Galois Correspondence for Compact Groups of Automorphisms of von Neumann Algebras with a Generalization to Kac Algebras
Abstract
Let
M
be a factor with separable predual and
G
a compact group of automorphisms of
M
whose action is minimal, i.e.
M
G
′
∩M=C
, where
M
G
denotes the
G
-fixed point subalgebra. Then every intemediate von Neumann algebra
M
G
⊂N⊂M
has the form
N=
M
H
for some closed subgroup
H
of
G
. An extension of this result to the case of actions of compact Kac algebras on factors is also presented. No assumptions are made on the existence of a normal conditional expectation onto
N
.