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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Finite decomposition rank for virtually nilpotent groups
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by Caleb Eckhardt, Elizabeth Gillaspy and Paul McKenney PDF
Trans. Amer. Math. Soc. 371 (2019), 3971-3994 Request permission

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 $2\cdot h(G)!-1$, 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.
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Additional Information
  • Caleb Eckhardt
  • Affiliation: Department of Mathematics, Miami University, Oxford, Ohio, 45056
  • MR Author ID: 885145
  • Email: eckharc@miamioh.edu
  • Elizabeth Gillaspy
  • Affiliation: Department of Mathematical Sciences, University of Montana, 32 Campus Drive # 0864, Missoula, Montana, 59812-0864
  • MR Author ID: 1107754
  • Email: elizabeth.gillaspy@mso.umt.edu
  • Paul McKenney
  • Affiliation: Department of Mathematics, Miami University, Oxford, Ohio, 45056
  • MR Author ID: 1024792
  • Email: mckennp2@miamioh.edu
  • Received by editor(s): July 21, 2017
  • Received by editor(s) in revised form: October 30, 2017
  • Published electronically: December 3, 2018
  • Additional Notes: 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 Universität Münster, Germany).
  • © Copyright 2018 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 3971-3994
  • MSC (2010): Primary 46L05; Secondary 20F19, 46L35, 46L55, 46L80
  • DOI: https://doi.org/10.1090/tran/7453
  • MathSciNet review: 3917214