Journal of Operator Theory

Volume 46, Issue 1, Summer 2001 pp. 25-38.

Structure of group

$C^*$ -algebras of Lie semi-direct products

${\bbb C}^n\rtimes {\bbb R}$

Authors: Takahiro Sudo
Author institution: Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus, Nishihara-cho, Okinawa 903--0213, Japan

Summary: In this paper we analyze the structure of group

$C^*$ -algebras of Lie semi-direct products of

$\Bbb C^n$ by

$\Bbb R$ to show that these

$C^*$ -algebras have finite composition series with their subquotients

$C^*$ -tensor products involving commutative

$C^*$ -algebras or the

$C^*$ -algebra of compact operators or noncommutative tori. As an application, we estimate stable rank and connected stable rank of these group

$C^*$ -algebras in terms of groups, and we deduce that group

$C^*$ -algebras of Lie semi-direct products of

$\Bbb R^n$ by

$\Bbb R$ have a similar structure as in the complex cases.

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