Abstract
Using fusion rules of sectors as a working hypothesis, we construct endomorphisms of the Cuntz algebra\(\mathcal{O}_n \) whose images have finite Watatani indices. Quasi-free KMS states on\(\mathcal{O}_n \) appear in a natural way associated with the endomorphisms, and we determine the Murray-von Neumann-Connes types of their GNS representations.
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Communicated by A. Jaffe
Dedicated to Huzihiro Araki
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Izumi, M. Subalgebras of infinite C*-algebras with finite Watatani indices I. Cuntz algebras. Commun.Math. Phys. 155, 157–182 (1993). https://doi.org/10.1007/BF02100056
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DOI: https://doi.org/10.1007/BF02100056