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On the geodesic distance and group actions on trees

Published online by Cambridge University Press:  24 October 2008

Marco Pavone
Marco Pavone
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, 10129, Torino, Italy
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Extract

The natural distance function on the vertices of a tree is a kernel of negative type. As a corollary, for any group G acting on a tree X, the length function |g| = d(υ, gυ) is a negative definite function on G for any given vertex υ of X.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 1 , July 1991 , pp. 67 - 70
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

‘1’Akemann, C. A. and Walter, M. E.. Unbounded negative definite functions. Canad. J. Math. 33 (1981), 862–871.Google Scholar
‘2’Alperin, R.. Locally compact groups acting on trees and property T. Monatsh. Math. 93 (1982), 261–265.Google Scholar
‘3’Berg, C., Christensen, J. P. R. and Ressel, P.. Harmonic Analysis on Semi groups. Graduate Texts in Math. no. 100 (Springer-Verlag, 1984).Google Scholar
‘4’Cartier, P.. Géométrie et analyse sur les arbres. In Sém. Bourbaki 1971é 407, Lecture Notes in Math. vol. 317 (Springer-Verlag, 1973), pp. 123–140.Google Scholar
‘5’Chiswell, I. M.. Abstract length functions in groups. Math. Proc. Cambridge Philos. Soc. 80 (1976), 451–463.CrossRefGoogle Scholar
‘6’Gromov, M.. Hyperbolic groups. In Essays in Group Theory (ed. Gersten, S. M.), MSRI publications vol. 8 (Springer-Verlag, 1987), pp. 75–263.Google Scholar
‘7’Haagerup, U.. An example of a non-nuclear C*-algebra which has the metric approximation property. Invent. Math. 50 (1979), 279–293.Google Scholar
‘8’Julg, P. and Valette, A.. K-Theoretic amenability for SL 2(ℚp), and the action on the associated tree. J. Funct. Anal. 58 (1984), 194–215.Google Scholar
‘9’Serre, J.-P.. Arbres, Amalgames, SL 2. Astérisque 46 (Soc. Math. France, 1977).Google Scholar
‘10’Watatani, Y.. Property T of Kazhdan implies property FA of Serre. Math. Japon. (1) 27 (1982), 97–103.Google Scholar