@article{4f81c92b5dd54191a6c480a448cd29b9,

title = "Finite decomposition rank for virtually nilpotent groups",

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.",

author = "Caleb Eckhardt and Elizabeth Gillaspy and Paul McKenney",

note = "Funding Information: The first author was partially supported by a grant from the Simons Foundation. The second author was primarily supported by the Deutsches Forschungsgemeinschaft via SFB 878 (awarded to the Universit{\"a}t M{\"u}nster, Germany). Funding Information: Received by the editors July 21, 2017, and, in revised form, October 30, 2017. 2010 Mathematics Subject Classification. Primary 46L05; Secondary 20F19, 46L35, 46L55, 46L80. The first author was partially supported by a grant from the Simons Foundation. The second author was primarily supported by the Deutsches Forschungsgemeinschaft via SFB 878 (awarded to the Universit{\"a}t M{\"u}nster, Germany). Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

year = "2019",

month = mar,

day = "15",

doi = "10.1090/tran/7453",

language = "English",

volume = "371",

pages = "3971--3994",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

number = "6",

}