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Classification of extensions of torus algebra. II. (English) Zbl 1253.46066
Summary: We use extension theory and algebraic methods to give a complete characterization of extensions of the torus algebra by stable Cuntz algebras, and prove certain classification theorems of these extension algebras.

MSC:
46L35 Classifications of \(C^*\)-algebras
46L05 General theory of \(C^*\)-algebras
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[1] Blackadar B. K-Theory for Operator Algebras. 2nd ed. Mathematical Sciences Research Institute Publications, 5. Cambridge: Cambridge University Press, 1998 · Zbl 0913.46054
[2] Brown L, Dadarlat M. Extensions of C*-algebras and quasidiagonality. J London Math Soc, 1996, 53: 582–600 · Zbl 0857.46045
[3] Elliott G A, Gong G. On the classification of C*-algebras of real rank zero. II. Ann of Math, 1996, 144: 497–610 · Zbl 0867.46041
[4] Elliott G A, Gong G. On inductive limits of matrix algebras over the two-torus. Amer J Math, 1996, 118: 263–290 · Zbl 0847.46032
[5] Elliott G A, Gong G, Li L. On the classification of simple inductive limit C*-algebras, II: The isomorphism theorem. Invent Math, 2007, 168: 249–320 · Zbl 1129.46051
[6] Elliott G A, Kucerovsky D. An abstract Brown-Douglas-Fillmore absorption theorem. Pacific J Math, 2001, 198: 385–409 · Zbl 1058.46041
[7] Gong G. On the classification of simple inductive limit C*-algebras, I: The reduction theorem. Doc Math, 2002, 7: 255–461 · Zbl 1024.46018
[8] Kirchberg E. The classification of purely infinite C*-algebras using Kasparovs theory. Preprint, 3rd draft, 1994
[9] Lin H. A classification theorem for infinite Toeplitz algebras. In: Operator Algebras and Operator Theory (Shanghai, 1997), Contemp Math, 228. Providence, RI: Amer Math Soc, 1998, 219–275
[10] Lin H. Classification of simple C*-algebras of tracial topological rank zero. Duke Math J, 2004, 125: 91–119 · Zbl 1068.46032
[11] Lin H. Classification of simple C*-algebras and higher dimensional noncommutative tori. Ann of Math, 2003, 157: 521–544 · Zbl 1049.46052
[12] Lin H. Simple nuclear C*-algebras of tracial topological rank one. J Funct Anal, 2007, 251: 601–679 · Zbl 1206.46052
[13] Lin H. Asymptotic unitary equivalence and classification of simple amenable C*-algebras. Invent Math, 2010, 183: 385–450 · Zbl 1255.46031
[14] Lin H, Su H. Classification of direct limits of generalized Toeplitz algebras. Pacific J Math, 1997, 181: 89–140 · Zbl 0905.46043
[15] MacLane S. Homology. Berlin: Springer-Verlag, 1963
[16] Phillips N C. A classification theorem for nuclear purely infinite simple C*-algebras. Doc Math, 2000, 5: 49–114 · Zbl 0943.46037
[17] Rordam M. Classification of extensions of certain C*-algebras by their six term exact sequences in K-theory. Math Ann, 1997, 308: 93–117 · Zbl 0874.46039
[18] Rordam M, Stormer E. Classification of Nuclear C*-Algebras. Entropy in Operator Algebras. Encyclopedia of Mathematical Sciences, 126. Heidelberg: Springer-Verlag, 2001
[19] Wei C. Universal coefficient theorems for the stable Ext-groups. J Funct Anal, 2010, 258: 650–664 · Zbl 1194.46103
[20] Wei C. Classification of extensions of $$A\(\backslash\)mathbb{T}$$ -algebras. Internat J Math, 2011, 22: 1187–1208 · Zbl 1232.46059
[21] Wei C, Wang L. Isomorphism of extensions of $$C\(\backslash\)left( {\(\backslash\)mathbb{T}\^2 } \(\backslash\)right)$$ . Sci China Math, 2011, 54: 281–286 · Zbl 1225.46051
[22] Wei C, Wang L. Hereditary subalgebras and comparisons of positive elements. Sci China Math, 2010, 53: 1565–1570 · Zbl 1200.46050
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