Stable Rank for Inclusions of C*-algebras
نویسنده
چکیده
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 a simple unital C*-algebra with tsr(A) = 1 and Property (SP), {Gk} n k=1 finite groups, αk actions from Gk to Aut((· · · ((A×α1 G1)×α2 G2) · · · )×αk−1 Gk−1). (G0 = {1}) Then tsr((· · · ((A×α1 G1)×α2 G2) · · · )×αn Gn) ≤ 2.
منابع مشابه
Topological Stable Rank of Inclusions of Unital C*-algebras
Let 1 ∈ A ⊂ B be an inclusion of C*-algebras of C*-index-finite type with depth 2. We try to compute topological stable rank of B (= tsr(B)) when A has topological stable rank one. We show that tsr(B) ≤ 2 when A is a tsr boundedly divisible algebra, in particular, A is a C*-minimal tensor product UHF ⊗ D with tsr(D) = 1. When G is a finite group and α is an action of G on UHF, we know that a cr...
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