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UCT-Kirchberg algebras have nuclear dimension one

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posted on 2024-11-16, 09:01 authored by Efren Ruiz, Aidan SimsAidan Sims, Adam Sorensen
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.

Funding

Operator algebras as models for dynamics and geometry

Australian Research Council

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Groupoids as bridges between algebra and analysis

Australian Research Council

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History

Citation

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

Journal title

Advances in Mathematics

Volume

279

Pagination

1

Language

English

RIS ID

100020

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