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Published: 
August 9, 2002

Keywords: 
group actions, trees, Ktheory, C*algebras.

Subject: 
Primary 20E08, 51E24; secondary 46L80

Abstract:

Let $T_1$ and $T_2$ be homogeneous trees of even degree $\ge 4$. A BM group $\Gamma$ is a torsionfree discrete subgroup of $\aut (T_1) \times \aut (T_2)$
which acts freely and transitively on the vertex set of $T_1 \times T_2$.
This article studies dynamical systems associated with BM groups.
A higher rank CuntzKrieger algebra $\mathcal A(\G)$ is associated both with a 2dimensional tiling system and with a boundary action of a BM group $\Gamma$. An explicit expression is given for the Ktheory of $\mathcal A(\G)$. In particular $K_0=K_1$.
A complete enumeration of possible BM groups $\G$ is given for a product homogeneous trees of degree 4, and the Kgroups are computed.

Acknowledgments:
This research was funded by the Australian Research Council. The second author is also grateful for the support of the University of Geneva.
Author information:
Mathematics Department, University of Newcastle, Callaghan, NSW 2308, Australia
guyan@maths.newcastle.edu.au
http://www.maths.newcastle.edu.au/~guyan/
jascki@iprimus.com.au
 