Examples of one-parameter automorphism groups of UHF algebras
نویسنده
چکیده
B. Blackadar [1] constructed for the first time an example of a symmetry (or an automorphism of period two) of the CAR algebra (or the UHF algebra of type 2) whose fixed point algebra is not AF (or approximately finite-dimensional). This was soon extended to produce an example of finite-group actions on UHF algebras whose fixed point algebras are not AF [5] and then of compact-group actions [12]. Note that these examples can now be obtained as corollaries [13, 4] to the classification results for certain amenable C-algebras started by G.A. Elliott [11] and extended by himself and many others (see e.g. [10]). In the same spirit we present yet other examples, this time, of one-parameter automorphism groups of UHF algebras, which do not seem to follow as a consequence from the above general results. Before stating what kind of examples they are we first recall the subject from [8, 3, 17]. Let A be a UHF algebra (or more generally, a simple AF C-algebra) and let α be a one-parameter automorphism group of A. We always assume that t 7→ αt(x) is continuous for each x ∈ A and denote by δ = δα the (infinitesimal) generator of α:
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تاریخ انتشار 2008