Some groups whose reduced C∗-algebras have stable rank one
نویسندگان
چکیده
منابع مشابه
Some Groups Whose Reduced C {algebras Have Stable Rank One
It is proved that, for the following classes of groups, ?, the reduced group C-algebra C (?) has stable rank 1: (i) hyperbolic groups which are either torsion{free and non{elementary or which are cocom-pact lattices in a real, noncompact, simple, connected Lie group of real rank 1 having trivial center; (ii) amalgamated free products of groups, ? = G 1 H G 2 , where H is nite and there is g 0 2...
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Abstract. We study the limits of inductive sequences (Ai, φi) where each Ai is a direct sum of full matrix algebras over compact metric spaces and each partial map of φi is diagonal. We give a new characterisation of simplicity for such algebras, and apply it to prove that the said algebras have stable rank one whenever they are simple and unital. Significantly, our results do not require any d...
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It is proved that the reduced group C∗-algebra C∗ red(G) has stable rank one (i.e. its group of invertible elements is a dense subset) if G is a discrete group arising as a free product G1 ∗G2 where |G1| ≥ 2 and |G2| ≥ 3. This follows from a more general result where it is proved that if (A, τ) is the reduced free product of a family (Ai, τi), i ∈ I, of unital C∗-algebras Ai with normalized fai...
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 1999
ISSN: 0021-7824
DOI: 10.1016/s0021-7824(99)00015-x