On the Classification of Simple Unital C*-algebras with Finite Decomposition Rank, Ii
نویسندگان
چکیده
Let A be a simple separable unital C*-algebra satisfying the UCT, and assume that A has finite decomposition rank. Let Q denote the UHF algebra with K0(Q) = Q. Then A⊗Q can be tracially approximated by unital Elliott-Thomsen algebras, and therefore A ⊗ Z is an ASH algebra (hence classifiable), where Z is the Jiang-Su algebra.
منابع مشابه
On the Classification of Simple Unital C*-algebras with Finite Decomposition Rank
Let A be a unital simple separable C*-algebra satisfying the UCT. Assume that dr(A) < +∞, A is Jiang-Su stable, and K0(A)⊗Q ∼= Q. Then A is an ASH algebra (indeed, A is a rationally AH algebra).
متن کاملDecomposition Rank and Z-stability
We show that separable, simple, nonelementary, unital C∗-algebras with finite decomposition rank absorb the Jiang–Su algebra Z tensorially. This has a number of consequences for Elliott’s program to classify nuclear C∗algebras by their K-theory data. In particular, it completes the classification of C∗-algebras associated to uniquely ergodic, smooth, minimal dynamical systems by their ordered K...
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 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 کاملA Note on Subhomogeneous C-algebras
We show that finitely generated subhomogeneous C∗-algebras have finite decomposition rank. As a consequence, any separable ASH C∗-algebra can be written as an inductive limit of subhomogeneous C∗-algebras each of which has finite decomposition rank. It then follows from work of H. Lin and of the second named author that the class of simple unital ASH algebras which have real rank zero and absor...
متن کامل