Classification of simple C*-algebras with unique traces

We classify certain almost multiplicative morphisms up to approximate unitary equivalence and use this result to prove the following: Let A and B be two unital separable simple C *-algebras of real rank zero, stable rank one, with weakly unperforated K 0 -groups and with unique normalized quasi-traces. Suppose that both A and B are locally AH and ( K * ( A ), K * ( A )+ ,[1 A ]) ≅ ( K * ( B ), K * ( B )+ ,[1 B ]). Then A is isomorphic to B .

[1]  Huaxin Lin,et al.  ALMOST MULTIPLICATIVE MORPHISMS AND K-THEORY , 2000 .

[2]  Huaxin Lin,et al.  Classification of Homomorphisms from C (X) to Simple C*-Algebras of Real Rank Zero , 2000 .

[3]  Huaxin Lin.  Extensions of C(X) by Simple C*-algebras of real rank zero , 1997 .

[4]  G. Gong.  On inductive limits of matrix algebras over higher dimensional spaces, part II. , 1997 .

[5]  Huaxin Lin,et al.  Classification of direct limits of generalized Toeplitz algebras , 1997 .

[6]  C. Pasnicu,et al.  Abelian \mathrm{C}^\ast-subalgebras of \mathrm{C}^\ast-algebras of real rank zero and inductive limit \mathrm{C}^\ast-algebras , 1996 .

[7]  G. Elliott,et al.  On the classification of C*-algebras of real rank zero, V , 1996, 1811.06758.

[8]  T. Loring,et al.  ClassifyingC*-algebras via ordered, mod-p K-theory , 1996 .

[9]  G. Elliott,et al.  On inductive limits of matrix algebras over the two-torus , 1996 .

[10]  Huaxin Lin.  Approximation by normal elements with finite spectra in C∗-algebras of real rank zero , 1996 .

[11]  M. Rørdam.  Classification of Certain Infinite Simple C*-Algebras , 1995 .

[12]  N. Phillips.  A classification theorem for nuclear purely infinite simple $C^*$-algebras , 1995, Documenta Mathematica.

[13]  Hongbing Su.  On the Classification of C*-Algebras of Real Rank Zero: Inductive Limits of Matrix Algebras over Non-Hausdorff Graphs , 1995 .

[14]  T. Loring,et al.  K-Homology, Asymptotic Representations, and Unsuspended E-Theory , 1994 .

[15]  G. Elliott,et al.  The structure of the irrational rotation C*-algebra , 1993 .

[16]  Huaxin Lin.  Exponential Rank of C*-Algebras with Real Rank Zero and the Brown-Pedersen Conjectures , 1993 .

[17]  Terry A. Loring,et al.  C*-Algebras Generated by Stable Relations , 1993 .

[18]  G. Pedersen,et al.  C∗-algebras of real rank zero , 1991 .

[19]  Claude L. Schochet,et al.  The Künneth theorem and the universal coefficient theorem for Kasparov’s generalized $K$-functor , 1987 .

[20]  B. Blackadar,et al.  K-Theory for Operator Algebras , 1986 .

[21]  Claude L. Schochet.  Topological methods for $C^{\ast}$-algebras. IV. Mod $p$ homology. , 1984 .

[22]  D. Handelman,et al.  Dimension functions and traces on C∗-algebras , 1982 .

[23]  G. Pedersen.  C-Algebras and Their Automorphism Groups , 1979 .

[24]  H. E. Jensen.  Scattered $C^*$-algebras II. , 1978 .

[25]  H. E. Jensen,et al.  Scattered $C^*$-algebras. , 1977 .

[26]  E. Effros,et al.  The completely positive lifting problem for C*-algebras , 1976 .

[27]  S. Mardešić.  On covering dimension and inverse limits of compact spaces , 1960 .

[28]  M. Dadarlat.  Reduction to dimension three of local spectra of real rank zero C*-algebras. , 1995 .

[29]  G. Elliott.  The Classification Problem for Amenable C*-Algebras , 1995 .

[30]  George A. Elliott,et al.  On the classification of C*-algebras of real rank zero. , 1993 .

[31]  M. Rørdam.  Classification of inductive limits of Cuntz algebras. , 1993 .

[32]  Huzihiro Araki,et al.  Quantum and Non-Commutative Analysis , 1993 .

[33]  G. Elliott.  A Classification of Certain Simple C*-Algebras , 1993 .

[34]  C. Akemann,et al.  Perfect C*-algebras , 1985 .

[35]  Edward G. Effros,et al.  Dimensions and C*-algebras , 1981 .