Irreducible inclusions of factors, multiplicative unitaries, and Kac algebras
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From an irreducible depth 2 inclusion of factors, verifying a regularity condition, we construct a multiplicative unitary, and an action, at every level of the canonical tower constructed from the inclusion; when this inclusion admits a faithful semi-finite normal operator-valued weight, stronger conditions are given, and the tower appears then as a crossed-product construction. In particular we rederive Herman and Ocneanu's results when the inclusion admits a faithful normal conditional expectation, and the tower is then the crossed-product construction, alternatively by a compact quantum group and by its dual, and, more precisely, according to Yamagami's result, by a compact type Kac algebra and by its dual.
Originalsprog | Engelsk |
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Tidsskrift | Journal of Functional Analysis |
Vol/bind | 137 |
Udgave nummer | 2 |
Sider (fra-til) | 466-543 |
Antal sider | 78 |
ISSN | 0022-1236 |
DOI | |
Status | Udgivet - 1 maj 1996 |
ID: 237365390