This paper proves that, among irreducible affine Weyl groups of rank at least two, every antipodal triple of ideal chambers is generic exactly for the types C2, G2, and B3.
Characterization of linear groups whose reduced C*-algebras are simple
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abstract
The reduced C*-algebra of a countable linear group G is shown to be simple if and only if G has no nontrivial normal amenable subgroups. Moreover, these conditions are shown to be equivalent to the uniqueness of tracial state on the aforementioned C*-algebra.
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The geometry of triples of antipodal ideal chambers of affine buildings
This paper proves that, among irreducible affine Weyl groups of rank at least two, every antipodal triple of ideal chambers is generic exactly for the types C2, G2, and B3.