AF-embeddability for Lie groups with $T_1$ primitive ideal spaces
| Autor: | Ingrid Beltiţă, Daniel Beltiţă |
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| Rok vydání: | 2020 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2004.11010 |
| Popis: | We study simply connected Lie groups $G$ for which the hull-kernel topology of the primitive ideal space $\text{Prim}(G)$ of the group $C^*$-algebra $C^*(G)$ is $T_1$, that is, the finite subsets of $\text{Prim}(G)$ are closed. Thus, we prove that $C^*(G)$ is AF-embeddable. To this end, we show that if $G$ is solvable and its action on the centre of $[G, G]$ has at least one imaginary weight, then $\text{Prim}(G)$ has no nonempty quasi-compact open subsets. We prove in addition that connected locally compact groups with $T_1$ ideal spaces are strongly quasi-diagonal. Comment: 23 pages, accepted for publication in J. London Math. Soc |
| Databáze: | OpenAIRE |
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