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ON THE STABLE RANK OF ALGEBRAS OF OPERATOR FIELDS OVER AN $N$-CUBE

Published online by Cambridge University Press:  28 April 2004

PING WONG NG  and
TAKAHIRO SUDO
PING WONG NG
Affiliation:
Department of Mathematics, University of Toronto, 100 St. George St., Room 4072, Toronto, Ontario, M5S 3G3, Canadapng@math.toronto.edu
TAKAHIRO SUDO
Affiliation:
Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus, Nishihara-cho, Okinawa, 903-0213, Japansudo@math.u-ryukyu.ac.jp
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Abstract

Let ${\cal A}$ be a unital maximal full algebra of operator fields with base space $[0, 1]^k$ and fibre algebras $\{{\cal A}_t\}_{t\in[0, 1]}^{k}$. It is shown in this paper that the stable rank of ${\cal A}$ is bounded above by the quantity sup$_{t\in[0, 1]^k}\,{\rm sr}(C([0, 1]^k)\,{\otimes}\,{\cal A}_t)$, where ‘sr’ means stable rank. Using the above estimate, the stable ranks of the C$^*$-algebras of the (possibly higher rank) discrete Heisenberg groups are computed.

Keywords

47L99
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 3 , May 2004 , pp. 358 - 364
Copyright
© The London Mathematical Society 2004

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