View paper:
 pdf dvi ps
View abstract:
 Abstract: Let $T_1$ and $T_2$ be homogeneous trees of even degree $\ge 4$. A BM group $\Gamma$ is a torsion-free 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 Cuntz-Krieger algebra $\mathcal A(\G)$ is associated both with a 2-dimensional tiling system and with a boundary action of a BM group $\Gamma$. An explicit expression is given for the K-theory 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 K-groups 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