Illinois Journal of Mathematics

Group actions on labeled graphs and their $C^{*}$-algebras

Teresa Bates, David Pask, and Paulette Willis

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We introduce the notion of the action of a group on a labeled graph and the quotient object, also a labeled graph. We define a skew product labeled graph and use it to prove a version of the Gross–Tucker theorem for labeled graphs. We then apply these results to the $C^{*}$-algebra associated to a labeled graph and provide some applications in non-Abelian duality.

Article information

Illinois J. Math., Volume 56, Number 4 (2012), 1149-1168.

First available in Project Euclid: 6 May 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L05: General theory of $C^*$-algebras
Secondary: 37B10: Symbolic dynamics [See also 37Cxx, 37Dxx]


Bates, Teresa; Pask, David; Willis, Paulette. Group actions on labeled graphs and their $C^{*}$-algebras. Illinois J. Math. 56 (2012), no. 4, 1149--1168. doi:10.1215/ijm/1399395826.

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