The Groups of Isometries of the Homogeneous Tree and Non-Unimodularity
Bollettino dell'Unione Matematica Italiana (2013)
- Volume: 6, Issue: 3, page 565-577
- ISSN: 0392-4041
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topNebbia, Claudio. "The Groups of Isometries of the Homogeneous Tree and Non-Unimodularity." Bollettino dell'Unione Matematica Italiana 6.3 (2013): 565-577. <http://eudml.org/doc/294020>.
@article{Nebbia2013,
abstract = {In this paper we describe the groups of isometries 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 isometries of a homogeneous tree of degree $q + 1 > 3$ which do not fix any point of the boundary of the tree.},
author = {Nebbia, Claudio},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {565-577},
publisher = {Unione Matematica Italiana},
title = {The Groups of Isometries of the Homogeneous Tree and Non-Unimodularity},
url = {http://eudml.org/doc/294020},
volume = {6},
year = {2013},
}
TY - JOUR
AU - Nebbia, Claudio
TI - The Groups of Isometries of the Homogeneous Tree and Non-Unimodularity
JO - Bollettino dell'Unione Matematica Italiana
DA - 2013/10//
PB - Unione Matematica Italiana
VL - 6
IS - 3
SP - 565
EP - 577
AB - In this paper we describe the groups of isometries 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 isometries of a homogeneous tree of degree $q + 1 > 3$ which do not fix any point of the boundary of the tree.
LA - eng
UR - http://eudml.org/doc/294020
ER -
References
top- FIGÀ-TALAMANCA, A. - NEBBIA, C., Harmonic analysis and representation theory for groups acting on homogeneous trees, London Mathematical Society Lecture Note Series, vol. 162, Cambridge University Press (Cambridge, 1991). Zbl1154.22301MR1152801DOI10.1017/CBO9780511662324
- GAAL, STEVEN A., Linear analysis and representation theory, Springer-Verlag (New York, 1973), Die Grundlehren der mathematischen Wissenschaften, Band 198. Zbl0275.43008MR447465
- NEBBIA, C., Amenability and Kunze-Stein property for groups acting on a tree, Pacific J. Math., 135, n. 2 (1988), 371-380. Zbl0671.43003MR968619
- TITS, J., Sur le groupe des automorphismes d'un arbre, Essays on topology and related topics (Mémoires dédiés à Georges de Rham), Springer (New York, 1970), 188-211. MR299534
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