Guihua Gong

ON THE CLASSIFICATION OF C*-ALGEBRAS OF REAL RANK ZERO, II

In this paper, we give a K-theoretic classification of real ranks zero inductive limits of generalized dimension drop interval algebras.

ALMOST MULTIPLICATIVE MORPHISMS AND K-THEORY

Let X be a compact metric space and A=C(X). Suppose that ℬ is a class of unital C*-algebras satisfying certain conditions, we prove the following: For any ∊>0, finite set F⊂A, there is an integer l such that if ϕ, ψ:A→B(B∈ℬ) are sufficiently multiplicative morphisms (e.g. when both ϕ and ψ are *-homomorphisms) which induce same K-theoretical maps, then there are a unitary u∈Ml+1(B) and a homomorphism σ:A→Ml(B) with finite dimensional image such that for all f∈F. In particular, the integer l does not depend on B, ϕ and ψ. This feature has important applications to the classification theory of nuclear C*-algebras.

Injectivity of the connecting maps in AH inductive limit systems

Let A be the inductive limit of a system A1 xrightarrow(phi1,2) A2 xrightarrow(phi2,3) A3 longrightarrow ... with An = bigoplusi=1tn Pn,i M[n,i](C(Xn,i))Pn,i, where Xn,i is a finite simplicial complex, and Pn,i is a projection in M[n,i](C(Xn,i)). In this paper, we will prove that A can be written as another inductive limit B1 xrightarrow(psi1,2) B2 xrightarrow(psi2,3) B3 longrightarrow ... with Bn = bigoplusi=1sn Qn,i M{n,i}(C(Yn,i)) Qn,i, where Yn,i is a finite simplicial complex, and Qn,i is a projection in M{n,i} (C(Yn,i)), with the extra condition that all the maps psin,n+1 are injective. (The result is trivial if one allows the spaces Yn,i to be arbitrary compact metrizable spaces.) This result is important for the classification of simple AH algebras. The special case that the spaces Xn,i are graphs is due to the third named author.

Determinant rank of C∗-algebras

Let

On the classification of simple inductive limit C ∗ -algebras, II: The isomorphism theorem

A

Abelian C*-subalgebras of C*-algebras of real rank zero and inductive limit C*-algebras

be a unital

ON INDUCTIVE LIMITS OF MATRIX ALGEBRAS OVER THE TWO-TORUS

C^*

Classification of finite simple amenable

-algebra and let

{\cal Z}

U_0(A)

-stable

be the group of unitaries of