Duality for actions of weak Kac algebras and crossed product inclusions of II_1 factors

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We show that indecomposable weak Kac algebras are free over their Cartan subalgebras and prove a duality theorem for their actions. Using this result, for any biconnected weak Kac algebra we construct a minimal action on the hyperfinite II_1 factor. The corresponding crossed product inclusion of II_1 factors has depth 2 and an integer index. Its first relative commutant is, in general, non-trivial, so we derive some arithmetic properties of weak Kac algebras from considering reduced subfactors.
Latex, 28 pages

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Quantum Algebra, Operator Algebras

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http://salesiana.dossiersoluciones.com/handle/123456789/77520

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9810049
 http://arxiv.org/abs/math/9810049

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arXiv