\newcommand{\Cc}{{\mathcal C}} \newcommand{\Hc}{{\mathcal H}} \newcommand{\Jc}{{\mathcal J}} \newcommand{\Kc}{{\mathcal K}} We prove that if a connected and simply connected Lie group $G$ admits connected closed normal subgroups $G_1\subseteq G_2\subseteq \cdots \subseteq G_m=G$ with dim\,$G_j=j$ for $j=1,\dots,m$, then its group $C^*$-algebra has closed two-sided ideals $\{0\}=\Jc_0\subseteq \Jc_1\subseteq\cdots\subseteq\Jc_n=C^*(G)$ with $\Jc_j/\Jc_{j-1}\simeq \Cc_0(\Gamma_j,\Kc(\Hc_j))$ for a suitable locally compact Hausdorff space $\Gamma_j$ and a separable complex Hilbert space $\Hc_j$, where $\Cc_0(\Gamma_j,\cdot)$ denotes the continuous mappings on $\Gamma_j$ that vanish at infinity, and $\Kc(\Hc_j)$ is the $C^*$-algebra of compact operators on $\Hc_j$ for $j=1,\dots,n$.
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Institute of Mathematics "Simion Stoilow", Romanian Academy, Bucharest, Romania
Ingrid Beltita; Daniel Beltita. The C*-Algebras of Completely Solvable Lie Groups are Solvable. Journal of Lie Theory, Tome 35 (2025) no. 4, pp. 719-736. http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a2/
@article{JOLT_2025_35_4_a2,
author = {Ingrid Beltita and Daniel Beltita},
title = {The {C*-Algebras} of {Completely} {Solvable} {Lie} {Groups} are {Solvable}},
journal = {Journal of Lie Theory},
pages = {719--736},
year = {2025},
volume = {35},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a2/}
}
TY - JOUR
AU - Ingrid Beltita
AU - Daniel Beltita
TI - The C*-Algebras of Completely Solvable Lie Groups are Solvable
JO - Journal of Lie Theory
PY - 2025
SP - 719
EP - 736
VL - 35
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a2/
ID - JOLT_2025_35_4_a2
ER -
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%A Daniel Beltita
%T The C*-Algebras of Completely Solvable Lie Groups are Solvable
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%D 2025
%P 719-736
%V 35
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2025_35_4_a2/
%F JOLT_2025_35_4_a2
