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A Furstenberg Transformation of the 2-Torus Without Quasi-Discrete Spectrum

Published online by Cambridge University Press:  20 November 2018

H. Rouhani
H. Rouhani*
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, B.C. V6T 1Y4
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Abstract

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R. Ji asked whether or not a Furstenberg transformation of the 2-torus of the form (x,y) → (e2πiθx, f(x)y), where θ is irrational and f : T —> T is continuous with non-zero degree k, is topologically conjugate to the Anzai transformation (x, y) → (e2πiθx, xk y) or its inverse. In this paper this question is settled in the negative. Further, some sufficient conditions are given under which the crossed product C*-algebra associated with a Furstenberg transformation of the 2-torus has a unique tracial state.

Keywords

46L80

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 3 , 01 September 1990 , pp. 316 - 322
Copyright
Copyright © Canadian Mathematical Society 1990

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