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STABLE RANK OF THE C*-ALGEBRAS OF SOLVABLE LIE GROUPS OF TYPE I

TAKAHIRO SUDO and HIROSHI TAKAI
Journal of Operator Theory
Vol. 38, No. 1 (Summer 1997), pp. 67-86
Published by: Theta Foundation
Stable URL: http://www.jstor.org/stable/24718831
Page Count: 20
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
STABLE RANK OF THE C*-ALGEBRAS OF SOLVABLE LIE GROUPS OF TYPE I
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Abstract

In this paper we show that the stable rank of the C*-algebras of simply-connected connected solvable Lie groups of type I is estimated by the complex dimension of the fixed point subspaces of the real dual spaces of their Lie algebras under the coadjoint actions. This result generalizes the estimation in the case of simply-connected connected nilpotent Lie groups. As corollaries, we show that the product formula of the stable rank holds for the C*-algebras of connected solvable Lie groups of type I, and estimate the real rank in the case of simply-connected connected solvable Lie groups of type I.

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