An official website of the United States government
Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to non-federal websites. Their policies may differ from this site.
-
Abstract We classify all essential extensions of the form $$ \begin{align*} &0 \rightarrow {\mathcal{W}} \rightarrow {D} \rightarrow A \rightarrow 0,\end{align*}$$where $${\mathcal {W}}$$ is the unique separable simple C*-algebra with a unique tracial state, which is $KK$-contractible and has finite nuclear dimension, and $$A$$ is a separable amenable $${\mathcal {W}}$$-embeddable C*-algebra, which satisfies the Universal Coefficient Theorem (UCT). We actually prove more general results. We also classify a class of amenable $C^*$-algebras, which have only one proper closed ideal $${\mathcal {W}}.$$more » « less
-
null (Ed.)The class of simple separable KK-contractible (KK-equivalent to \{0\} ) C*-algebra s which have finite nuclear dimension is shown to be classified by the Elliott invariant. In particular, the class of C*-algebras A\otimes K is classifiable, where A is a simple separable C*-algebra with finite nuclear dimension and is the simple inductive limit of Razak algebras with unique trace, which is boundedmore » « less
-
Elliott, G.A. (Ed.)A classification theorem is obtained for a class of unital simple separable amenable Z-stable C*-algebras which exhausts all possi- ble values of the Elliott invariant for unital stably finite simple separable amenable Z-stable C*-algebras. Moreover, it contains all unital simple separable amenable C∗-algebras which satisfy the UCT and have finite rational tracial rank.more » « less
-
Elliott, G.A. (Ed.)A class of C*-algebras, to be called those of generalized tracial rank one, is introduced. A second class of unital simple separable amenable C*-algebras, those whose tensor products with UHF-algebras of infinite type are in the first class, to be referred to as those of rational generalized tracial rank one, is proved to exhaust all possible values of the Elliott invariant for unital finite simple separable amenable Z-stable C*- algebras. A number of results toward the classification of the second class are presented including an isomorphism theorem for a special sub-class of the first class, leading to the general classification of all unital simple C*- algebras with rational generalized tracial rank one in Part II.more » « less
-
null (Ed.)We present a classification theorem for separable amenable simple stably projectionless C -algebras with finite nuclear dimension whose K0 vanish on traces which satisfy the Universal Coefficient Theorem. One of C -algebras in the class is denoted by Z0 which has a unique tracial state, K_0(Z_0) = Z and K1(Z_0) = {0}. Let A and B be two separable amenable simple C -algebras satisfying the UCT. We show that A ⊗ Z_0 = B ⊗ Z_0 if and only if Ell(A ⊗ Z_0 ) = Ell(B ⊗ Z_0 ). A class of simple separable C -algebras which are approximately sub-homogeneous whose spectra having bounded dimension is shown to exhaust all possible Elliott invariant for C -algebras of the form A ⊗ Z_0 , where A is any finite separable simple amenable C -algebras.more » « less
-
We study a class of stably projectionless simple C*-algebras which may be viewed as having generalized tracial rank one in analogy with the unital case. Some struc- tural questions concerning these simple C*-algebras are studied. The paper also serves as a technical support for the classification of separable stably projectionless simple amenable Jiang-Su stable C*-algebras.more » « less
Full Text Available