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

D. Nikshych
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Abstract

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.

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BibTeXRIS

D. Nikshych. 1998-10-08. Duality for actions of weak Kac algebras and crossed product inclusions of II_1 factors. https://arxiv.org/abs/math/9810049

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