The Classification of Separable Simple C*-algebras Which Are Inductive Limits of Continuous-trace C*-algebras with Spectrum Homeomorphic to the Closed Interval [0,1]
نویسندگان
چکیده
A classification is given of certain separable nuclear C*algebras not necessarily of real rank zero, namely, the class of separable simple C*-algebras which are inductive limits of continuoustrace C*-algebras whose building blocks have spectrum homeomorphic to the closed interval [0, 1], or to a disjoint union of copies of this space. Also, the range of the invariant is calculated. 1991 Mathematics Subject Classification. 46L35, 46L06.
منابع مشابه
On the Classification of Simple Approximately Subhomogeneous C*-algebras Not Necessarily of Real Rank Zero
A classification is given of certain separable nuclear C*-algebras not necessarily of real rank zero, namely the class of simple C*-algebras which are inductive limits of continuous-trace C*-algebras whose building blocks have their spectrum homeomorphic to the interval [0, 1] or to a finite disjoint union of closed intervals. In particular, a classification of those stably AI algebras which ar...
متن کاملDERIVATIONS OF TENSOR PRODUCT OF SIMPLE C*-ALGEBRAS
In this paper we study the properties of derivations of A B, where A and B are simple separable C*-algebras, and A B is the C*-completion of A B with respect to a C*-norm Yon A B and we will characterize the derivations of A B in terms of the derivations of A and B
متن کاملOn a functional equation for symmetric linear operators on $C^{*}$ algebras
Let $A$ be a $C^{*}$ algebra, $T: Arightarrow A$ be a linear map which satisfies the functional equation $T(x)T(y)=T^{2}(xy),;;T(x^{*})=T(x)^{*} $. We prove that under each of the following conditions, $T$ must be the trivial map $T(x)=lambda x$ for some $lambda in mathbb{R}$: i) $A$ is a simple $C^{*}$-algebra. ii) $A$ is unital with trivial center and has a faithful trace such ...
متن کاملAsymptotically Unitary Equivalence and Classification of Simple Amenable C∗-algebras
Let C and A be two unital separable amenable simple C-algebras with tracial rank no more than one. Suppose that C satisfies the Universal Coefficient Theorem and suppose that φ1, φ2 : C → A are two unital monomorphisms. We show that there is a continuous path of unitaries {ut : t ∈ [0,∞)} of A such that lim t→∞ u∗tφ1(c)ut = φ2(c) for all c ∈ C if and only if [φ1] = [φ2] in KK(C,A), φ ‡ 1 = φ 2 ...
متن کاملThe Range of a Class of Classifiable Separable Simple Amenable C-algebras
We study the range of a classifiable class A of unital separable simple amenable C∗algebras which satisfy the Universal Coefficient Theorem. The class A contains all unital simple AH-algebras. We show that all unital simple inductive limits of dimension drop circle C∗-algebras are also in the class. This unifies some of the previous known classification results for unital simple amenable C∗-alg...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008