JournalsprimsVol. 13, No. 3pp. 777–791

On the Fixed Point Algebra of a UHF Algebra under a Periodic Automorphism of Product Type

  • Akitaka Kishimoto

    Kyoto University, Japan
On the Fixed Point Algebra of a UHF Algebra under a Periodic Automorphism of Product Type cover
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Abstract

We study the fixed point algebra &" of a UHF algebra 21 under a periodic automorphism a of product type. We show an example of lawhichissimpleandhasmorethantwotracialstatesandwecharacterizethecasewhere91hasonlyonetracialstate.Nextweshowthatla which is simple and has more than two tracial states and we characterize the case where 91* has only one tracial state. Next we show that iff is a UHF algebra if and only if 21 is generated by an infinite family of mutually commuting a-invariant type IP subfactors whose fixed point algebras are abelian and by a UHF subalgebra of 21" which commutes with the former (where p denotes the period of a).

Cite this article

Akitaka Kishimoto, On the Fixed Point Algebra of a UHF Algebra under a Periodic Automorphism of Product Type. Publ. Res. Inst. Math. Sci. 13 (1977), no. 3, pp. 777–791

DOI 10.2977/PRIMS/1195189607