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On stably finiteness for \(C^*\)-algebras of exponential solvable Lie groups

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We study the link between stably finiteness and stably projectionless-ness for \(C^*\)-algebras of solvable Lie groups. We show that these two properties are equivalent if the dimension of the group is not divisible by 4; otherwise, they are not necessarily equivalent. To provide examples proving the last assertion, we study exponential solvable Lie groups that have nonempty finite open sets in their unitary dual.

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Acknowledgements

We wish to thank the Referee for several remarks that improved the presentation. The research of the second-named author was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS/CCCDI - UEFISCDI, project number PN-III-P4-ID-PCE-2020-0878, within PNCDI III.

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  1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania

    Ingrid Beltiţă & Daniel Beltiţă

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  1. Ingrid Beltiţă
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  2. Daniel Beltiţă
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Correspondence to Daniel Beltiţă.

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Beltiţă, I., Beltiţă, D. On stably finiteness for \(C^*\)-algebras of exponential solvable Lie groups. Math. Z. 304, 2 (2023). https://doi.org/10.1007/s00209-023-03256-z

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