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A comment on certain p–shift algebras

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  09 April 2009

P. J. Stacey
P. J. Stacey
Affiliation:
La Trobe UniversityBundooraVictoria 3083, Australia
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Abstract

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Let G = ⊕∞i=0Zp, where p is a prime, let s be the shift mapping the i th summand of G to the (i+1) st and let ω be a 2 cocycle on G with values in S1, for which ω (s(g), s(h)) = ω (g, h). If Ω (ej, ek) = Ω (ek, ej) whenever │j - k│ is sufficiently large, where ei is the generator of the i th summand of G, then it is shown that the twisted group C* -algebra C*(G, ω) 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 on UHF (p∞).

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras 46L40: Automorphisms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 1 , August 1990 , pp. 55 - 58
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Bures, D., and Yin, H. S., ‘Shifts on the hyperfinite factor of type II1’, J. Operator Theory 20 (1988), 91–106.Google Scholar
[2]Enomoto, M., Nagisa, M., Watatani, Y. and Yoshida, H., ‘Relative commutant algebras of Powers', binary shifts on the hyperfinite II1 factor’, preprint, 1988.Google Scholar
[3]Karpilovsky, G., Projective representation of finite groups, (Marcel Dekker, 1985).Google Scholar
[4]Powers, R. T., ‘An index theory for semigroups of *-endomorphisms of B(H) and type II1 factors’, Canad. J. Math. 40 (1988), 86–114.CrossRefGoogle Scholar