Journal of Operator Theory

Volume 49, Issue 1, Winter 2003 pp. 25-44.

Type III actions on boundaries of $\tilde A_n$ buildings

Authors: Paul Cutting (1) and Guyan Robertson (2)
Author institution: (1) Mathematics Department, University of Newcastle, Callaghan, NSW, Australia
(2) Mathematics Department, University of Newcastle, Callaghan, NSW, Australia

Summary: Let $\Gamma$ be a group of type rotating automorphisms of a building $\mathcal X$ of type $\tilde A_n$ and order $q$. Suppose that $\Gamma$ acts freely and transitively on the vertex set of $\mathcal X$. Then the action of $\Gamma$ on the boundary of $\mathcal X$ is ergodic, of type $\rm III_{1/q}$ or type $\rm III_{1/{q^2}}$ depending on whether $n$ is odd or even.

Keywords: affine building, boundary action, type III factor

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