We study the fixed point algebra &" of a UHF algebra 21 under a periodic automorphism a of product type. We show an example of 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. 777–791DOI 10.2977/PRIMS/1195189607