Finite decomposition rank for virtually nilpotent groups

Caleb Eckhardt, Elizabeth Gillaspy, Paul McKenney

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)3971-3994
Number of pages24
JournalTransactions of the American Mathematical Society
Volume371
Issue number6
DOIs
StatePublished - Mar 15 2019

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