Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T11:26:36.822Z Has data issue: false hasContentIssue false
  • English
  • Français

On groups with real valued length function

Published online by Cambridge University Press:  24 October 2008

A. H. M. Hoare
A. H. M. Hoare
Affiliation:
Department of Mathematics, University of Birmingham
Get access Rights & Permissions [Opens in a new window]

Extract

Groups with length functions were introduced by Lyndon [5], and those with integer valued length were shown by Chiswell [2] to be equivalent to groups acting on trees, investigated by Serre[6]. Watatani[7] showed that for a group with integer valued length function the edges of the tree form an orthonormal set in a Hilbert space on which the group acts as a group of isometries.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 2 , March 1984 , pp. 223 - 227
Copyright
Copyright © Cambridge Philosophical Society 1984

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Akemann, C. A. and Walter, M.. Unbounded negative definite functions. Canad. J. Math. 23 (1981), 862–871.CrossRefGoogle Scholar
[2]Chiswell, I. M.. Abstract length functions in groups. Math. Proc. Cambridge Philos. Soc. 80 (1976), 451–463.CrossRefGoogle Scholar
[3]Delorme, P.. 1-Cohomologie des représentations unitaires. Bull Soc. Math. France 105 (1977), 281–336.CrossRefGoogle Scholar
[4]Imrich, W.. On metric properties of tree-like spaces. Beiträge zur Graphentheorie und deren Anwendungen, Oberhof (DDR) (ed. Sektion, Marök der Technischen Hochschule Ilmenau), pp. 129–156.Google Scholar
[5]Lyndon, R. C.. Length functions in groups. Math. Scand. 12 (1963), 209–234.CrossRefGoogle Scholar
[6]Serre, J.-P.. Trees (Springer-Verlag, 1980).CrossRefGoogle Scholar
[7]Watatani, Y.. Property T of Kazhdan implies property FA of Serre. Math. Japon. 27 (1982), 99–103.Google Scholar