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Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs

Journal Article


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Abstract


  • In a previous work, the authors showed that the C*-algebra C*(\Lambda) of a row-finite higher-rank graph \Lambda with no sources is simple if and only if \Lambda is both cofinal and aperiodic. In this paper, we generalise this result to row-finite higher-rank graphs which are locally convex (but may contain sources). Our main tool is Farthing's "removing sources" construction which embeds a row-finite locally convex higher-rank graph in a row-finite higher-rank graph with no sources in such a way that the associated C*-algebras are Morita equivalent.

UOW Authors


  •   Robertson, Dave I. (external author)
  •   Sims, Aidan

Publication Date


  • 2009

Citation


  • Robertson, D. & Sims, A. (2009). Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs. Israel Journal of Mathematics, 172 171-192.

Scopus Eid


  • 2-s2.0-77949580900

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1797&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/783

Number Of Pages


  • 21

Start Page


  • 171

End Page


  • 192

Volume


  • 172

Place Of Publication


  • http://www.springerlink.com/content/g61475wn7785p20g/fulltext.pdf

Abstract


  • In a previous work, the authors showed that the C*-algebra C*(\Lambda) of a row-finite higher-rank graph \Lambda with no sources is simple if and only if \Lambda is both cofinal and aperiodic. In this paper, we generalise this result to row-finite higher-rank graphs which are locally convex (but may contain sources). Our main tool is Farthing's "removing sources" construction which embeds a row-finite locally convex higher-rank graph in a row-finite higher-rank graph with no sources in such a way that the associated C*-algebras are Morita equivalent.

UOW Authors


  •   Robertson, Dave I. (external author)
  •   Sims, Aidan

Publication Date


  • 2009

Citation


  • Robertson, D. & Sims, A. (2009). Simplicity of C*-algebras associated to row-finite locally convex higher-rank graphs. Israel Journal of Mathematics, 172 171-192.

Scopus Eid


  • 2-s2.0-77949580900

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1797&context=infopapers

Ro Metadata Url


  • http://ro.uow.edu.au/infopapers/783

Number Of Pages


  • 21

Start Page


  • 171

End Page


  • 192

Volume


  • 172

Place Of Publication


  • http://www.springerlink.com/content/g61475wn7785p20g/fulltext.pdf