# zbMATH — the first resource for mathematics

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
##### Keywords:
torus algebra; extension; isomorphism
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.