Representations of compact quantum groups and subfactors

Details Representations of compact quantum groups and subfactors Representations of compact quantum groups and subfactors

1998-04-03

arxiv.org/abs/math/9804015v2

J. Reine Angew. Math. 509 (1999), 167-198

Mathematics

Quantum Algebra

39 pages, Latex; a few typos were corrected; version to be published by Crelle's Journal

Scientific paper

We associate Popa systems (= standard invariants of subfactors) to the finite dimensional representations of compact quantum groups. We characterise the systems arising in this way: these are the ones which can be ``represented'' on finite dimensional Hilbert spaces. This is proved by an universal construction. We explicitely compute (in terms of some free products) the operation of going from representations of compact quantum groups to Popa systems and then back via the universal construction. We prove a Kesten type result for the co-amenability of compact quantum groups, which allows us to compare it with the amenability of subfactors.

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