Simple AH-algebras of real rank zero

作者: Huaxin Lin

DOI: 10.1090/S0002-9939-03-06995-8

关键词: Discrete mathematicsDimension (vector space)Simple (abstract algebra)Rank (linear algebra)Rank of an abelian groupZero (complex analysis)UnitalMathematicsPure mathematics

摘要: Let A be a unital simple AH-algebra with real rank zero. It is shown that if satisfies so-called fundamental comparison property, then has tracial topological Combining some previous results, it zero, stable one and weakly unperforated K 0 (A) must have slow dimension growth.

参考文章(17)
Huaxin Lin, Homomorphisms from $C^*$-algebras of continuous trace Mathematica Scandinavica. ,vol. 86, pp. 249- 272 ,(2000) , 10.7146/MATH.SCAND.A-14292
Bruce Blackadar, K-Theory for Operator Algebras ,(1986)
George A. Elliott, Guihua Gong, Huaxin Lin, Cornel Pasnicu, Abelian C∗-subalgebras of C∗-algebras of real rank zero and inductive limit C∗-algebras Duke Mathematical Journal. ,vol. 85, pp. 511- 554 ,(1996) , 10.1215/S0012-7094-96-08520-8
Huaxin Lin, Tracially AF *-algebras Transactions of the American Mathematical Society. ,vol. 353, pp. 693- 722 ,(2000) , 10.1090/S0002-9947-00-02680-5
Bruce Blackadar, David Handelman, Dimension functions and traces on C∗-algebras Journal of Functional Analysis. ,vol. 45, pp. 297- 340 ,(1982) , 10.1016/0022-1236(82)90009-X
George A. Elliott, Guihua Gong, ON THE CLASSIFICATION OF C*-ALGEBRAS OF REAL RANK ZERO, II Annals of Mathematics. ,vol. 144, pp. 497- 610 ,(1996) , 10.2307/2118565
K. R. Goodearl, Notes on a class of simple $C^*$-algebras with real rank zero Publicacions Matematiques. ,vol. 36, pp. 637- 654 ,(1992) , 10.5565/PUBLMAT_362A92_23
Huaxin Lin, Classification of Simple Tracially AF C -Algebras Canadian Journal of Mathematics. ,vol. 53, pp. 161- 194 ,(2001) , 10.4153/CJM-2001-007-8
Jesper Villadsen, Simple C*-Algebras with Perforation Journal of Functional Analysis. ,vol. 154, pp. 110- 116 ,(1998) , 10.1006/JFAN.1997.3168
Huaxin Lin, Classification of simple C*-algebras of tracial topological rank zero Duke Mathematical Journal. ,vol. 125, pp. 91- 119 ,(2004) , 10.1215/S0012-7094-04-12514-X