Rokhlin dimension for C*-correspondences

Nathanial P. Brown, Aaron Tikuisis, Aleksey M. Zelenberg

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1 Citation (Scopus)

Abstract

We extend the notion of Rokhlin dimension from topological dynamical systems to C∗-correspondences. We show that in the presence of finite Rokhlin dimension and a mild quasidiagonal-like condition (which, for example, is automatic for finitely generated projective correspondences), finite nuclear dimension passes from the scalar algebra to the associated Toeplitz–Pimsner and (hence) Cuntz–Pimsner algebras. As a consequence we provide new examples of classifiable C∗-algebras: if A is simple, unital, has finite nuclear dimension and satisfies the UCT, then for every finitely generated projective H with finite Rokhlin dimension, the associated Cuntz–Pimsner algebra O(H) is classifiable in the sense of Elliott’s Program.
Original languageEnglish
Pages (from-to)613-643
Number of pages31
JournalHouston Journal of Mathematics
Volume44
Issue number2
Publication statusPublished - 2018

Keywords

  • Nuclear C∗-algebras
  • C∗-correspondences
  • nuclear dimension
  • Rokhlin property
  • Rokhlin dimension

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    Brown, N. P., Tikuisis, A., & Zelenberg, A. M. (2018). Rokhlin dimension for C*-correspondences. Houston Journal of Mathematics, 44(2), 613-643. https://arxiv.org/abs/1608.03214v1