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arXiv · 1210.4050

On groups with quasidiagonal C*-algebras

José Carrión·Marius Dadarlat·Caleb Eckhardt
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Abstract

We examine the question of quasidiagonality for C*-algebras of discrete amenable groups from a variety of angles. We give a quantitative version of Rosenberg's theorem via paradoxical decompositions and a characterization of quasidiagonality for group C*-algebras in terms of embeddability of the groups. We consider several notable examples of groups, such as topological full groups associated with Cantor minimal systems and Abels' celebrated example of a finitely presented solvable group that is not residually finite, and show that they have quasidiagonal C*-algebras. Finally, we study strong quasidiagonality for group C*-algebras, exhibiting classes of amenable groups with and without strongly quasidiagonal C*-algebras.

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José Carrión, Marius Dadarlat, Caleb Eckhardt. 2012-10-15. On groups with quasidiagonal C*-algebras. https://arxiv.org/abs/1210.4050

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