Tokyo Journal of Mathematics

Structure of the $C^*$-Algebras of Nilpotent Lie Groups

Takahiro SUDO

Abstract

We show that the algebraic structure of the group $C^*$-algebra $C^*(G)$ of a simply connected, connected nilpotent Lie group $G$ is described as repeating finitely the extension of $C^*$-algebras with $T_{2^-}$ spectrums by themselves and one more extension by a commutative $C^*$-algebra on the fixed point space $(\mathfrak{G}^*)^G$ of $\mathfrak{G}^*$ under the coadjoint action of $G$. Using this result, we show that $C^*(G)$ has no non-trivial projections.

Article information

Source
Tokyo J. Math., Volume 19, Number 1 (1996), 211-220.

Dates
First available in Project Euclid: 31 March 2010

https://projecteuclid.org/euclid.tjm/1270043230

Digital Object Identifier
doi:10.3836/tjm/1270043230

Mathematical Reviews number (MathSciNet)
MR1391939

Zentralblatt MATH identifier
0866.22010

Citation

SUDO, Takahiro. Structure of the $C^*$-Algebras of Nilpotent Lie Groups. Tokyo J. Math. 19 (1996), no. 1, 211--220. doi:10.3836/tjm/1270043230. https://projecteuclid.org/euclid.tjm/1270043230