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

$\fX$ of type

$\wt A_n$ and order

$q$ . Suppose that

$\G$ acts freely and transitively on the vertex set of

$\fX$ . Then the action of

$\Gamma$ on the boundary of

$\fX$ is ergodic, of type

$\tq$ or type

$\tqs$ depending on whether

$n$ is odd or even.

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