Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 7 (2012), 27 -- 30

A KAZHDAN GROUP WITH AN INFINITE OUTER AUTOMORPHISM GROUP

Traian Preda

Abstract. D. Kazhdan has introduced in 1967 the Property (T) for local compact groups (see [3]). In this article we prove that for n ≥ 3 and m ∈ ℕ the group SL_n (K)⋉ℳ_n,m(K) is a Kazhdan group having the outer automorphism group infinite.

2010 Mathematics Subject Classification: 22D10; 22D45.
Keywords: Representations of topological groups; Kazhdan Property (T); Mautner's lemma.

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References

1. B. Bekka, P. de la Harpe, A. Valette, Kazhdan's Property (T), Monography, Cambridge University Press, 2008. MR2415834.

2. P. de la Harpe, A. Valette, La propriété (T) de Kazhdan pour les groupes localement compacts, Astérisque 175, Soc. Math. France, 1989. MR1023471(90m:22001). Zbl 0759.22001.

3. D. Kazhdan, Connection of the dual space of a group with the structure of its closed subgroups, Funct. Anal. Appl. 1 (1967), 63 - 657. MR209390. Zbl 0168.27602.

Traian Preda
University of Bucharest,
Str. Academiei nr.14, Bucureşti,
Romania.
e-mail: traianpr@yahoo.com

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