Displaying similar documents to “Bounded generation and Kazhdan’s property ( T ) ”

The Novikov conjecture for linear groups

Erik Guentner, Nigel Higson, Shmuel Weinberger (2005)

Publications Mathématiques de l'IHÉS

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Let K be a field. We show that every countable subgroup of GL(,K) is uniformly embeddable in a Hilbert space. This implies that Novikov’s higher signature conjecture holds for these groups. We also show that every countable subgroup of GL(2,K) admits a proper, affine isometric action on a Hilbert space. This implies that the Baum-Connes conjecture holds for these groups. Finally, we show that every subgroup of GL(,K) is exact, in the sense of C-algebra theory.

Valuations and group algebras

Ulrich Albrecht, Günter Törner (1998)

Rendiconti del Seminario Matematico della Università di Padova

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Explicit Kazhdan constants for representations of semisimple and arithmetic groups

Yehuda Shalom (2000)

Annales de l'institut Fourier

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Consider a simple non-compact algebraic group, over any locally compact non-discrete field, which has Kazhdan’s property ( T ) . For any such group, G , we present a Kazhdan set of two elements, and compute its best Kazhdan constant. Then, settling a question raised by Serre and by de la Harpe and Valette, explicit Kazhdan constants for every lattice Γ in G are obtained, for a “geometric” generating set of the form Γ ∩ B r , where B r ⊂ G is a ball of radius r , and the dependence of r on Γ is described...

Conjugacy and factorization results on matrix groups

Thomas Laffey (1994)

Banach Center Publications

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In this survey paper, we present (mainly without proof) a number of results on conjugacy and factorization in general linear groups over fields and commutative rings. We also present the additive analogue in matrix rings of some of these results. The first section deals with the question of expressing elements in the commutator subgroup of the general linear group over a field as (simple) commutators. In Section 2, the same kind of problem is discussed for the general linear group over...