Stable rank and real rank for some classes of group $C^\ast $-algebras
نویسندگان
چکیده
منابع مشابه
Stable Rank and Real Rank of Graph C ∗ - Algebras
For a row finite directed graph E, Kumjian, Pask, and Rae-burn proved that there exists a universal C *-algebra C * (E) generated by a Cuntz-Krieger E-family. In this paper we consider two density problems of invertible elements in graph C *-algebras C * (E), and it is proved that C * (E) has stable rank one, that is, the set of all invertible elements is dense in C * (E) (or in its unitization...
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Abstract. When a unital C*-algebra A has topological stable rank one (write tsr(A) = 1), we know that tsr(pAp) ≤ 1 for a non-zero projection p ∈ A. When, however, tsr(A) ≥ 2, it is generally faluse. We prove that if a unital C*algebra A has a simple unital C*-subalgebra D of A with common unit such that D has Property (SP) and supp∈P (D) tsr(pAp) < ∞, then tsr(A) ≤ 2. As an application let A be...
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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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2005
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-05-03835-3