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Quasidiagonality of \(C^*\)-Algebras of Solvable Lie Groups

  • Ingrid Beltiţă
  • Daniel Beltiţă
Article
  • 38 Downloads

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.

Keywords

Unitary dual \(ax+b\)-Group Solvable Lie group Quasidiagonal \(C^*\)-algebra 

Mathematics Subject Classification

Primary 22D25 Secondary 22E27 

Notes

Acknowledgements

We wish to thank the referee for carefully reading of our manuscript and several remarks that improved the presentation.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania

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