A Galois Correspondence for Compact Groups of Automorphisms of von Neumann Algebras with a Generalization to Kac Algebras

Abstract

LetMbe a factor with separable predual andGa compact group of automorphisms ofMwhose action is minimal, i.e.,MG′∩M=C, whereMGdenotes theG-fixed point subalgebra. Then every intermediate von Neumann algebraMG⊂N⊂Mhas the formN=MHfor some closed subgroupHofG. 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 ontoN. © 1998 Academic Press.