The nuclear dimension of graph C*-algebras

2013/12/02 by Efren Ruiz, Ruiz, Efren, Aidan Sims +3 · 2 citations
Mathematics · #46L35 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L35

paper · pdf · doi:10.48550/arxiv.1312.0507

24 pages; this version to appear in Adv. Math

arxiv created 2014/11/24 · arxiv updated 2014/11/26

Abstract

Consider a graph C*-algebra C*(E) with a purely infinite ideal I (possibly all of C*(E)) such that I has only finitely many ideals and C*(E)/I is approximately finite dimensional. We prove that the nuclear dimension of C*(E) is 1. If I has infinitely many ideals, then the nuclear dimension of C*(E) is either 1 or 2.

Cited by

• Z-stable Graph Algebras
• Nuclear dimension, pure infiniteness and real rank for higher rank graph C^*-algebras

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