In this paper we describe the groups of isometrics acting transitively on the homogeneous tree of degree three. This description implies that the following three properties are equivalent: amenability, non-unimodularity and action without inversions. Moreover, we exhibit examples of non-unimodular transitive groups of isometrics of a homogeneous tree of degree q + 1 > 3 which do not fix any point of the boundary of the tree.
The groups of isometries of the homogeneous tree and non-unimodularity / Nebbia, Claudio. - In: BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA. - ISSN 1972-6724. - STAMPA. - 6:3(2013), pp. 565-577.
The groups of isometries of the homogeneous tree and non-unimodularity
NEBBIA, Claudio
2013
Abstract
In this paper we describe the groups of isometrics acting transitively on the homogeneous tree of degree three. This description implies that the following three properties are equivalent: amenability, non-unimodularity and action without inversions. Moreover, we exhibit examples of non-unimodular transitive groups of isometrics of a homogeneous tree of degree q + 1 > 3 which do not fix any point of the boundary of the tree.File allegati a questo prodotto
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