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Structure theory and stable rank for C*-algebras of finite higher-rank graphs

Published online by Cambridge University Press:  04 October 2021

David Pask
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, WollongongNSW2522, Australia(dpask@uow.edu.au; asierako@uow.edu.au; asims@uow.edu.au)
Adam Sierakowski
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, WollongongNSW2522, Australia(dpask@uow.edu.au; asierako@uow.edu.au; asims@uow.edu.au)
Aidan Sims
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, WollongongNSW2522, Australia(dpask@uow.edu.au; asierako@uow.edu.au; asims@uow.edu.au)

Abstract

We study the structure and compute the stable rank of $C^{*}$-algebras of finite higher-rank graphs. We completely determine the stable rank of the $C^{*}$-algebra when the $k$-graph either contains no cycle with an entrance or is cofinal. We also determine exactly which finite, locally convex $k$-graphs yield unital stably finite $C^{*}$-algebras. We give several examples to illustrate our results.

Type
Research Article
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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