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Groups acting on products of trees, tiling systems and analytic K-theory

Lookup NU author(s): Professor Guyan Robertson

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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.

Publication metadata

Author(s): Robertson G; Kimberley JS

Publication type: Article

Publication status: Published

Journal: New York J. Math.

Year: 2002

Volume: 8

Pages: 111-131

ISSN (electronic): 1076-9803

Publisher: Electronic Journals Project

URL: http://nyjm.albany.edu:8000/j/2002/8-7.pdf

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