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Geometry of a crossed product

Author: Igor Nikolaev
Journal: Proc. Amer. Math. Soc. 128 (2000), 1177-1183
MSC (1991): Primary 46L40, 57R30, 58F10
Published electronically: October 18, 1999
MathSciNet review: 1654101
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Abstract: We introduce a continuous dimension function $\alpha: \bullet\to\mathbb{R}$ on the Grothendieck group $K_0$ over the crossed product $C^*$-algebra $C(X)\rtimes _{\phi}\mathbb{Z}$. The function $\alpha$ has an elegant geometry: on every minimal flow $\phi^t$ it takes the value of the ``rotation number" of $\phi^t$; such a problem was posed in 1936 by A. Weil.

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Additional Information

Igor Nikolaev
Affiliation: CRM, Université de Montréal, Montréal H3C 3J7, Canada; Fields Institute, 222 College Stree, Toronto, Canada M5T 3J1

Keywords: Dimension group, continued fraction, minimal flow
Received by editor(s): November 14, 1997
Received by editor(s) in revised form: June 17, 1998
Published electronically: October 18, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society