Topological Stable Rank of Inclusions of Unital C*-algebras
نویسنده
چکیده
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 crossed product algebra UHF ⋊α G has topological stable rank less than or equal to two. These results are affirmative datum to a generalization of a question by B. Blackadar in 1988.
منابع مشابه
Stable Rank for Inclusions of C*-algebras
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...
متن کاملIsomorphisms in unital $C^*$-algebras
It is shown that every almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...
متن کاملAlgebras with Locally Finite Decomposition
We introduce the notion of locally finite decomposition rank, a structural property shared by many stably finite nuclear C∗-algebras. The concept is particularly relevant for Elliott’s program to classify nuclear C∗algebras by K-theory data. We study some of its properties and show that a simple unital C∗-algebra, which has locally finite decomposition rank, real rank zero and which absorbs the...
متن کاملVarious topological forms of Von Neumann regularity in Banach algebras
We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...
متن کاملOn the Classification of Simple Z-stable C-algebras with Real Rank Zero and Finite Decomposition Rank
We show that, if A is a separable simple unital C-algebra which absorbs the Jiang–Su algebra Z tensorially and which has real rank zero and finite decomposition rank, then A is tracially AF in the sense of Lin, without any restriction on the tracial state space. As a consequence, the Elliott conjecture is true for the class of C-algebras as above which, additionally, satisfy the Universal Coeff...
متن کامل