C*-simplicity of free products with amalgamation and radical classes of groups

Abstract

We give new characterizations to ensure that a free product of groups with amalgamation has a simple reduced group C*-algebra, and provide a concrete example of an amalgam with trivial kernel, such that its reduced group C*-algebra has a unique tracial state, but is not simple. Moreover, we show that there is a radical class of groups for which the reduced group C*-algebra of any group is simple precisely when the group has a trivial radical corresponding to this class.

23 pages; the statement of Lemma 5.8 and the proof of Theorem 5.9 have been corrected, and certain paragraphs of Section 5 have been reformulated to accommodate for this

References in corpus (3)

• Boundaries of reduced C*-algebras of discrete groups
• An intrinsic characterization of C*-simplicity
• Subgroup dynamics and $C^{\ast }$-simplicity of groups of homeomorphisms

Cited by in corpus (3)

• An intrinsic characterization of C*-simplicity
• C*-irreducibility for reduced twisted group C*-algebras
• Two Families of Examples of Groups Acting on Trees with Nontrivial Quasi-Kernels