Embedding an AH-Algebra into a Simple C^*-Algebra with Prescribed KK-Data

Lin, Huaxin

Department of Mathematics, East China Normal University, Shanghai, China and Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, U.S.A. e-mail: [email protected]

K-Theory 24(2):p 135-156, October 2001.

Let X be a connected finite CW complex. We show that, given a positive homomorphism α∈ Hom(K_*(C(X)), K_*(A)) with α[1_C(X)]≤[1_A], where A is a unital separable simple C^*-algebra with real rank zero, stable rank one and weakly unperforated K₀(A), there exists a homomorphism h: C(X)→A such that h induces α. We also prove a structure result for unital separable simple C^*-algebras A with real rank zero, stable rank one and weakly unperforated K₀(A), namely, there exists a simple AH-algebra of real rank zero contained in A which determines the K-theory of A.

Embedding an AH-Algebra into a Simple C*-Algebra with Prescribed KK-Data

Embedding an AH-Algebra into a Simple C^*-Algebra with Prescribed KK-Data