Structure of the $C^*$-Algebras of Nilpotent Lie Groups
SUDO, Takahiro
Tokyo J. of Math., Tome 19 (1996) no. 2, p. 211-220 / Harvested from Project Euclid
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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.
Publié le : 1996-06-15
Classification:  
@article{1270043230,
     author = {SUDO, Takahiro},
     title = {Structure of the $C^*$-Algebras of Nilpotent Lie Groups},
     journal = {Tokyo J. of Math.},
     volume = {19},
     number = {2},
     year = {1996},
     pages = { 211-220},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1270043230}
}

SUDO, Takahiro. Structure of the $C^*$-Algebras of Nilpotent Lie Groups. Tokyo J. of Math., Tome 19 (1996) no. 2, pp.  211-220. http://gdmltest.u-ga.fr/item/1270043230/