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UCT-Kirchberg algebras have nuclear dimension one

Journal Article


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Abstract


  • We prove that every Kirchberg algebra in the UCT class has nuclear dimension 1. We first show that Kirchberg 2-graph algebras with trivial K0 and finite K1 have nuclear dimension 1 by adapting a technique developed by Winter and Zacharias for Cuntz algebras. We then prove that every Kirchberg algebra in the UCT class is a direct limit of 2-graph algebras to obtain our main theorem.

UOW Authors


  •   Ruiz, Efren (external author)
  •   Sims, Aidan
  •   Sorensen, Adam P. (external author)

Publication Date


  • 2015

Citation


  • Ruiz, E., Sims, A. & Sorensen, A. P. (2015). UCT-Kirchberg algebras have nuclear dimension one. Advances in Mathematics, 279 1-28.

Scopus Eid


  • 2-s2.0-84927733106

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5165&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4144

Has Global Citation Frequency


Number Of Pages


  • 27

Start Page


  • 1

End Page


  • 28

Volume


  • 279

Place Of Publication


  • United Kingdom

Abstract


  • We prove that every Kirchberg algebra in the UCT class has nuclear dimension 1. We first show that Kirchberg 2-graph algebras with trivial K0 and finite K1 have nuclear dimension 1 by adapting a technique developed by Winter and Zacharias for Cuntz algebras. We then prove that every Kirchberg algebra in the UCT class is a direct limit of 2-graph algebras to obtain our main theorem.

UOW Authors


  •   Ruiz, Efren (external author)
  •   Sims, Aidan
  •   Sorensen, Adam P. (external author)

Publication Date


  • 2015

Citation


  • Ruiz, E., Sims, A. & Sorensen, A. P. (2015). UCT-Kirchberg algebras have nuclear dimension one. Advances in Mathematics, 279 1-28.

Scopus Eid


  • 2-s2.0-84927733106

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=5165&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/4144

Has Global Citation Frequency


Number Of Pages


  • 27

Start Page


  • 1

End Page


  • 28

Volume


  • 279

Place Of Publication


  • United Kingdom