The $C^*$-algebras of completely solvable Lie groups are solvable
| Autor: | Beltita, Ingrid, Beltita, Daniel |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $\{0\}=\mathcal{J}_0\subseteq \mathcal{J}_1\subseteq\cdots\subseteq\mathcal{J}_n=C^*(G)$ with $\mathcal{J}_j/\mathcal{J}_{j-1}\simeq \mathcal{C}_0(\Gamma_j,\mathcal{K}(\mathcal{H}_j))$ for a suitable locally compact Hausdorff space $\Gamma_j$ and a separable complex Hilbert space $\mathcal{H}_j$, where $\mathcal{C}_0(\Gamma_j,\cdot)$ denotes the continuous mappings on $\Gamma_j$ that vanish at infinity, and $\mathcal{K}(\mathcal{H}_j)$ is the $C^*$-algebra of compact operators on $\mathcal{H}_j$ for $j=1,\dots,n$. Comment: 17 pages |
| Databáze: | arXiv |
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