$C^\ast$-simple groups without free subgroups

Autor:	Olshanskii, A. Yu., Osin, D. V.
Rok vydání:	2014
Předmět:	Mathematics - Group Theory Mathematics - Operator Algebras 20F06 20F67 22D25 47L05
Druh dokumentu:	Working Paper
Popis:	We construct first examples of non-trivial groups without non-cyclic free subgroups whose reduced $C^\ast$-algebra is simple and has unique trace. This answers a question of de la Harpe. Both torsion and torsion free examples are provided. In particular, we show that the reduced $C^\ast$-algebra of the free Burnside group $B(m,n)$ of rank $m\ge 2$ and any sufficiently large odd exponent $n$ is simple and has unique trace.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1401.7300 Zobrazit plný text záznamu View this record from Arxiv