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

✍ Scribed by Masaki Izumi; Roberto Longo; Sorin Popa

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 493 KB
Volume: 155
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1997.3228

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✦ Synopsis

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 intermediate 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.

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