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.
Citation
Takahiro SUDO. "Structure of the $C^*$-Algebras of Nilpotent Lie Groups." Tokyo J. Math. 19 (1) 211 - 220, June 1996. https://doi.org/10.3836/tjm/1270043230
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