Inclusions irréductibles de facteurs et unitaires multiplicatifs, II

✍ Scribed by Michel Enock

• Book ID: 102972374
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 557 KB
• Volume: 154
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1997.3206

✦ Synopsis

From an irreducible depth 2 inclusion M 0 /M 1 of factors with a faithful semifinite normal operator-valued weight, verifying a regularity condition, we construct the canonical tower (M i ) i # N . We prove then that both relative commutants M 2 & M$ 0 and M 3 & M$ 1 bear Woronowicz algebra structures, dual to each other, as defined by Masuda and Nakagami. Moreover, there exists an outer action of M 3 & M$ 1 on M 1 , such that M 0 is the fixed-point algebra and M 2 is the crossedproduct. The tower appears then as the tower of successive crossed-products.

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