## Illinois Journal of Mathematics

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

#### Abstract

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

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

Dates
First available in Project Euclid: 6 May 2014

https://projecteuclid.org/euclid.ijm/1399395826

Digital Object Identifier
doi:10.1215/ijm/1399395826

Mathematical Reviews number (MathSciNet)
MR3231477

Zentralblatt MATH identifier
1292.46034

Subjects
Primary: 46L05: General theory of $C^*$-algebras

#### Citation

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. https://projecteuclid.org/euclid.ijm/1399395826

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