Representations of minimally almost periodic groups

Journal of the Australian Mathematical Society

Alain Valette¹ 

关键词: 22 D 12;    secondary 20 G 15;    46 L 05;   

DOI  :  10.1017/S1446788700033838

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

For any group G, we introduce the subset S(G) of elements g which are conjugate tofor some positive integer k. We show that, for any bounded representation π of G any g in S(G), either π(g) = 1 or the spectrum of π(g) is the full unit circle in C. As a corollary, S(G) is in the kernel of any homomorphism from G to the unitary group of a post-liminal C*-algebra with finite composition series.Next, for a topological group G, we consider the subset of elements approximately conjugate to 1, and we prove that it is contained in the kernel of any uniformly continuous bounded representation of G, and of any strongly continuous unitary representation in a finite von Neumann algebra.We apply these results to prove triviality for a number of representations of isotropic simple algebraic groups defined over various fields.

【 授权许可】

Unknown