J Austral Math Soc Ser A 49 pp55--58, 1990.

A Comment on Certain p-Shift Algebras

P. J. Stacey

(Received 20 March 1989)

Abstract

Let G = Å^¥_i=0Z_p, where p is prime, let s be the shift mapping the ith summand of G to the (i + 1)st and let w be a 2 cocycle on G with values in S¹, for which w(s(g), s(h)) = w(g, h). If w(e_j, e_k) = w(e_k, e_j) whenever |j - k| is sufficiently large, where e_i is the generator of the ith summand of G, then it is shown that the twisted group C*-algebra C*(G, w) is isomorphic to the UHF algebra UHF(p^¥). An immediate consequence, by results of Bures and Yin, is the existence of infinitely many non-conjugate shifts of UHF(p^¥).

1980 AMS Subject Classification (1985 Revision): 46L05, 46L40

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Authors

P. J. Stacey: La Trobe University, Bundoora, Victoria 3083, Australia.

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Last Modified: Wed Feb 19 10:27:52 2003