Compact group actions on UHF algebras obtained by folding the interval

Evans, David Emrys and Kishimoto, Akitaka 1991. Compact group actions on UHF algebras obtained by folding the interval. Journal of Functional Analysis 98 (2) , pp. 346-360. 10.1016/0022-1236(91)90082-G

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Abstract

We show that for any integer p greater than one, there exists a C-∗ algebra , which is not AF, such that Mp∞⊗A≃Mp∞, where Mpα = Mp⊗ ∞ is the UHF algebra of type p∞. Using this construction of UHF algebras, as inductive limits of subhomogeneous algebras on an interval, embedded in each other via a folding operation on the interval, we exhibit actions of compact groups on UHF algebras whose fixed point algebras are not AF. In particular for any compact group G ≠ {e}, there exists an action of G on Mp∞ whose fixed point algebra is not AF.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Elsevier
ISSN:	0022-1236
Last Modified:	04 Jul 2024 08:44
URI:	https://orca.cardiff.ac.uk/id/eprint/32972

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