سند علمی

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

چکیده

Let M be a factor with separable predual and G a compact group of automorphisms of M whose action is minimal, i.e. M ′ ∩M = C, where M denotes the G-fixed point subalgebra. Then every intemediate von Neumann algebra M ⊂ N ⊂ M has the form N = M 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 . ∗ Miller Research Fellow. ∗∗ Supported in part by MURST and CNR-GNAFA. ∗∗∗ Supported in part by NSF Grant DMS-9206984.

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