A GALOIS CORRESPONDENCE FOR COMPACT-GROUPS OF AUTOMORPHISMS OF VON-NEUMANN-ALGEBRAS WITH A GENERALIZATION TO KAC ALGEBRAS

Let M be a factor with separable predual and G a compact group of auto morphisms of M whose action is minimal, i.e., M-G' boolean AND M = C, where M-G denotes the G-fixed point subalgebra. Then every intermediat e von Neumann algebra M-G subset of N subset of M has the form N=M-H f or some closed subgroup H of G. An extension of this result to the cas e of actions of compact Kac algebras on factors is also presented. No assumptions are made on the existence of a normal conditional expectat ion onto N. (C) 1998 Academic Press.