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On simplicity of reduced C*‐algebras of groups
Author(s) -
de la Harpe Pierre
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdl014
Subject(s) - mathematics , countable set , simplicity , simple (philosophy) , abelian group , pure mathematics , group (periodic table) , simple group , exposition (narrative) , classification of finite simple groups , algebra over a field , simple module , group theory , group of lie type , art , philosophy , chemistry , literature , organic chemistry , epistemology
A countable group is C*‐simple if its reduced C*‐algebra is a simple algebra. Since Powers recognised in 1975 that non‐abelian free groups are C*‐simple, large classes of C*‐simple groups which appear naturally in geometry have been identified, including non‐elementary Gromov hyperbolic groups and lattices in semisimple groups. In this exposition, C*‐simplicity for countable groups is viewed as an extreme case of non‐amenability. The basic examples are described, and several open problems are formulated.