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Aperiodicity and cofinality for finitely aligned higher-rank graphs

Journal Article


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Abstract


  • We introduce new formulations of aperiodicity and cofinality for finitely aligned higher-rank graphs $\Lambda$, and prove that $C^*(\Lambda)$ is simple if and only if $\Lambda$ is aperiodic and cofinal. The main advantage of our versions of aperiodicity and cofinality over existing ones is that ours are

    stated in terms of finite paths. To prove our main result, we first characterise each of aperiodicity and cofinality of $\Lambda$ in terms of the ideal structure of $C^*(\Lambda)$. In an appendix we show how our new cofinality condition simplifies in a number of special cases which have been treated previously in the literature; even in these settings our results are new.

UOW Authors


Publication Date


  • 2010

Citation


  • Lewin, P. & Sims, A. (2010). Aperiodicity and cofinality for finitely aligned higher-rank graphs. Cambridge Philosophical Society: Mathematical Proceedings, 149 (2), 333-350.

Scopus Eid


  • 2-s2.0-77957226016

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1838&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/825

Number Of Pages


  • 17

Start Page


  • 333

End Page


  • 350

Volume


  • 149

Issue


  • 2

Abstract


  • We introduce new formulations of aperiodicity and cofinality for finitely aligned higher-rank graphs $\Lambda$, and prove that $C^*(\Lambda)$ is simple if and only if $\Lambda$ is aperiodic and cofinal. The main advantage of our versions of aperiodicity and cofinality over existing ones is that ours are

    stated in terms of finite paths. To prove our main result, we first characterise each of aperiodicity and cofinality of $\Lambda$ in terms of the ideal structure of $C^*(\Lambda)$. In an appendix we show how our new cofinality condition simplifies in a number of special cases which have been treated previously in the literature; even in these settings our results are new.

UOW Authors


Publication Date


  • 2010

Citation


  • Lewin, P. & Sims, A. (2010). Aperiodicity and cofinality for finitely aligned higher-rank graphs. Cambridge Philosophical Society: Mathematical Proceedings, 149 (2), 333-350.

Scopus Eid


  • 2-s2.0-77957226016

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1838&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/825

Number Of Pages


  • 17

Start Page


  • 333

End Page


  • 350

Volume


  • 149

Issue


  • 2