Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 11
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Farsi, Carla Gillaspy, Elizabeth Kang, Sooran and Packer, Judith A. 2016. Separable representations, KMS states, and wavelets for higher-rank graphs. Journal of Mathematical Analysis and Applications, Vol. 434, Issue. 1, p. 241.


    an Huef, Astrid Laca, Marcelo Raeburn, Iain and Sims, Aidan 2015. KMS states on the <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mo>⁎</mml:mo></mml:mrow></mml:msup></mml:math>-algebra of a higher-rank graph and periodicity in the path space. Journal of Functional Analysis, Vol. 268, Issue. 7, p. 1840.


    Laca, Marcelo Larsen, Nadia S. Neshveyev, Sergey Sims, Aidan and Webster, Samuel B. G. 2015. Von Neumann algebras of strongly connected higher-rank graphs. Mathematische Annalen, Vol. 363, Issue. 1-2, p. 657.


    Maloney, Ben Pask, David and Raeburn, Iain 2014. Skew-products of higher-rank graphs and crossed products by semigroups. Semigroup Forum, Vol. 88, Issue. 1, p. 162.


    Brownlowe, Nathan Sims, Aidan and Vittadello, Sean T. 2013. Co-universal C*-algebras associated to generalised graphs. Israel Journal of Mathematics, Vol. 193, Issue. 1, p. 399.


    Yi, Inhyeop 2013. -Algebras from Groupoids on Self-Similar Groups. Abstract and Applied Analysis, Vol. 2013, p. 1.


    Yi, Inhyeop 2013. Asymptotic -Algebras from -Actions on Higher Rank Graphs. Abstract and Applied Analysis, Vol. 2013, p. 1.


    Yi, In-Hyeop 2012. DYNAMICAL SYSTEMS AND GROUPOID ALGEBRAS ON HIGHER RANK GRAPHS. The Pure and Applied Mathematics, Vol. 19, Issue. 2, p. 199.


    PASK, DAVID RAEBURN, IAIN and WEAVER, NATASHA A. 2009. A family of 2-graphs arising from two-dimensional subshifts. Ergodic Theory and Dynamical Systems, Vol. 29, Issue. 05, p. 1613.


    Marrero, Alberto E. and Muhly, Paul S. 2008. Groupoid and inverse semigroup presentations of ultragraph C *-algebras. Semigroup Forum, Vol. 77, Issue. 3, p. 399.


    MUHLY, PAUL S. and TOMFORDE, MARK 2005. TOPOLOGICAL QUIVERS. International Journal of Mathematics, Vol. 16, Issue. 07, p. 693.


    ×
  • Ergodic Theory and Dynamical Systems, Volume 23, Issue 4
  • August 2003, pp. 1153-1172

Actions of $\mathbb{Z}^k$ associated to higher rank graphs

  • ALEX KUMJIAN (a1) and DAVID PASK (a2)
  • DOI: http://dx.doi.org/10.1017/S0143385702001670
  • Published online: 01 August 2003
Abstract

An action of $\mathbb{Z}^k$ is associated to a higher rank graph $\Lambda$ satisfying a mild assumption. This generalizes the construction of a topological Markov shift arising from a non-negative integer matrix. We show that the stable Ruelle algebra of $\Lambda$ is strongly Morita equivalent to $C^*(\Lambda)$. Hence, if $\Lambda$ satisfies the aperiodicity condition, the stable Ruelle algebra is simple, stable and purely infinite.

Copyright
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax