## Abstract

We show that inductive limits of virtually nilpotent groups have strongly quasidiagonal C*-algebras, extending results of the first author on solvable virtually nilpotent groups. We use this result to show that the decomposition rank of the group C*-algebra of a finitely generated virtually nilpotent group G is bounded by 2·h(G)!−1, where h(G) is the Hirsch length of G. This extends and sharpens results of the first and third authors on finitely generated nilpotent groups. It then follows that if a C*-algebra generated by an irreducible representation of a virtually nilpotent group satisfies the universal coefficient theorem, it is classified by its Elliott invariant.

Original language | English |
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Pages (from-to) | 3971-3994 |

Number of pages | 24 |

Journal | Transactions of the American Mathematical Society |

Volume | 371 |

Issue number | 6 |

DOIs | |

State | Published - Mar 15 2019 |