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On tracial approximation. (English) Zbl 1137.46035
Let T be a tree with finitely many vertices {v i } i=1 n and let (k ¯ i ={k i1 ,,k ij i }) i=1 n be n partitions of an integer k, with all numbers non-zero. The splitting tree algebra S(k ¯ 1 ,,k ¯ n ;T) is the algebra of all continuous M k ()-valued functions f on T such that f(v i )M k i1 ()M k ij i () for all i. Let 𝒮 be a class of splitting tree algebras and let TA𝒮 be the class of C * -algebras that can be tracially approximated by the C * -algebras in 𝒮. Let A be a simple separable C * -algebra in TA𝒮. It is shown that there exists a simple inductive limit C * -algebra B of C * -algebras in the class 𝒮 ' consisting of 𝒮 together with the Gong standard homogeneous C * -algebras such that the Elliott invariant of A is isomorphic to the Elliott invariant of B.

46L35Classifications of C * -algebras
46L05General theory of C * -algebras
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