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Tracial Limit of C^＊-algebras 被引量：12

Tracial Limit of C*-algebras
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摘要 A new limit of C*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C*-algebra A is a tracial limit of C*-algebras in I^(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits. A new limit of C*-algebras, the tracial limit, is introduced in this paper. We show that a separable simple C*-algebra A is a tracial limit of C*-algebras in I^(k) if and only if A has tracial topological rank no more than k. We present several known results using the notion of tracial limits.
作者 ShanWenHU HuaXinLIN YiFengXUE
机构地区 DepartmentofMathematics DepartmentofMathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2003年第3期535-556,共22页 数学学报（英文版）
关键词 Tracial limit Tracial topological rank Tracial limit Tracial topological rank
分类号 O177.5 [理学—基础数学]
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参考文献15

  • 1Hu, S., Lin, H., Xue, Y.: The tracial topological rank for C^*-algebras (Ⅱ). preprint.
  • 2Lin, H.: Tracial AF C^*-algebras. Trans. Amer. Math. Soc., 353, 693-722 (2001).
  • 3Lin, H.: Classification of simple TAF C^*-algebras, Canad. J. Math., 53, 161-194 (2001).
  • 4Cuntz, J.: The structure of addition and multiplication in simple C^*-algebras. Math. Scand., 40: 215-233(1977).
  • 5Cuntz, J.: Dimension functions on simple C^*-algebras. Math. Ann., 233, 145-153 (1978).
  • 6Dadarlat, M., Nagy, G., Nemethi, A., Pasnica, C.: Reduction of topological stable rank in inductive limits of C^*-algebras. Pacific J. Math., 153, 267-276 (1992).
  • 7Lin, H.: The tracial topological rank for C^*-algebras. Proc. London Math. Soc., 83(3), 199-234 (2001).
  • 8Blackdar, B., Dadarlat, M., Rordam, M.: Thereal rank in inductive limits of C~*-algebras. Mathl Scand.,69, 211-216 (1991).
  • 9Lin, H.: Calssification of simple C^*-algebras of tracial topological rank zero. MSRI, preprint (2000).
  • 10Blackdar, B.: K-theory for operator algebras, Spring-Verlag, New York (1986).

同被引文献8

  • 1姚洪亮,胡善文.具有迹实秩零的C~*-代数(英文)[J].华东师范大学学报（自然科学版）,2004(2):5-12. 被引量：1
  • 2肖翔,胡善文.C~*-代数迹极限性质的封闭性(英文)[J].华东师范大学学报（自然科学版）,2006(3):8-14. 被引量：1
  • 3LIN H.The tracial topological rank of C*-algebras[J].Proc London Math Soc,2001,83(1):199-234.
  • 4LIN H.Tracially AF C*-algebras[J].Trans Amer Math Soc,2001,353:693-722.
  • 5HU S,Lin H,XUE Y.The tracial topological rank of extensions of C*-algebras[J].Math Scand,2004,94(1):125-147.
  • 6BLACKADAR B.Comparison theory for simple C*-algebras[C]//EVANS D,TAKESAKI M.Operator Algebras and Applications.Cambridge:Cambridge Univ Press,1989:21-54.
  • 7LIN H.An Introduction to the Classification of Amenable C*-Algebras[M].New Jersey:World Scientific,2001.
  • 8刘树冬,方小春.纯无限单C~*-代数的扩张代数的K-理论Ⅱ[J].数学年刊（A辑）,2009,30(3):433-438. 被引量：1

引证文献12

二级引证文献3

Acta Mathematica Sinica,English Series
2003年 第3期

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