Rokhlin dimension for C*-correspondences

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

Research output: Contribution to journalArticle

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

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Correspondence
Algebra
Finitely Generated
Unital
C*-algebra
Dynamical system
Scalar

Keywords

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

Cite this

Brown, N. P., Tikuisis, A., & Zelenberg, A. M. (2018). Rokhlin dimension for C*-correspondences. Houston Journal of Mathematics, 44(2), 613-643.

Rokhlin dimension for C*-correspondences. / Brown, Nathanial P.; Tikuisis, Aaron; Zelenberg, Aleksey M.

In: Houston Journal of Mathematics, Vol. 44, No. 2, 2018, p. 613-643.

Research output: Contribution to journalArticle

Brown, NP, Tikuisis, A & Zelenberg, AM 2018, 'Rokhlin dimension for C*-correspondences', Houston Journal of Mathematics, vol. 44, no. 2, pp. 613-643.
Brown NP, Tikuisis A, Zelenberg AM. Rokhlin dimension for C*-correspondences. Houston Journal of Mathematics. 2018;44(2):613-643.
Brown, Nathanial P. ; Tikuisis, Aaron ; Zelenberg, Aleksey M. / Rokhlin dimension for C*-correspondences. In: Houston Journal of Mathematics. 2018 ; Vol. 44, No. 2. pp. 613-643.
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author = "Brown, {Nathanial P.} and Aaron Tikuisis and Zelenberg, {Aleksey M.}",
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AU - Tikuisis, Aaron

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