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Bulletin of the London Mathematical Society Advance Access originally published online on March 20, 2008
Bulletin of the London Mathematical Society 2008 40(2):217-226; doi:10.1112/blms/bdn001
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© 2008 London Mathematical Society

Realization of a simple higher-dimensional noncommutative torus as a transformation group C*-algebra

Benjamín A. Itzá-Ortiz

Centro de Investigación en Matemáticas
Universidad Autónoma del Estado de Hidalgo
Pachuca de Soto Hidalgo 42184
México

N. Christopher Phillips

Department of Mathematics
University of Oregon
Eugene, OR 97403-1222
USA
ncp@darkwing.uoregon.edu

Received 15 May 2007.

Let {theta} be a nondegenerate skew symmetric real dxd matrix, and let A{theta} be the corresponding simple higher-dimensional noncommutative torus. Suppose that d is odd, or that d≥4 and the entries of {theta} are not contained in a quadratic extension of Q. Then A{theta} is isomorphic to the transformation group C*-algebra obtained from a minimal homeomorphism of a compact connected one-dimensional space locally homeomorphic to the product of the interval and the Cantor set. The proof uses classification theory of C*-algebras.

2000 Mathematics Subject Classification 46L55 (primary), 46L35, 54H20 (secondary).

Reasearch of the first author is partially supported by CONACYT grant 050233. Research of the second author is partially supported by NSF grant DMS 0302401.


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