Abstract
We characterize the solvable Lie groups of the form \({\mathbb {R}}^m\rtimes {\mathbb {R}}\), whose \(C^*\)-algebras are quasidiagonal. Using this result, we determine the connected simply connected solvable Lie groups of type I whose \(C^*\)-algebras are strongly quasidiagonal. As a by-product, we give also examples of amenable Lie groups with non-quasidiagonal \(C^*\)-algebras.
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We wish to thank the referee for carefully reading of our manuscript and several remarks that improved the presentation.
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This work was supported by a Grant of the Romanian National Authority for Scientific Research and Innovation, CNCS–UEFISCDI, Project Number PN-II-RU-TE-2014-4-0370.
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Beltiţă, I., Beltiţă, D. Quasidiagonality of \(C^*\)-Algebras of Solvable Lie Groups. Integr. Equ. Oper. Theory 90, 5 (2018). https://doi.org/10.1007/s00020-018-2438-6
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DOI: https://doi.org/10.1007/s00020-018-2438-6