On the inductive limit of direct sums of simple TAI algebras

2019/05/28 by Bo Cui, Chunlan Jiang, Cui, Bo +3
Mathematics · #FOS: Mathematics #Operator Algebras (math.OA) #math.OA

paper · pdf · doi:10.48550/arxiv.1905.12451

24 pages. arXiv admin note: text overlap with arXiv:1607.07581

arxiv created 2019/05/28 · arxiv updated 2019/05/30

Abstract

An ATAI (or ATAF, respectively) algebra, introduced in [Jiang1] (or in [Fa] respectively) is an inductive limit lim_n→∞(A_n=\bigoplus_i=1A_nⁱ,ϕ_nm), where each A_nⁱ is a simple separable nuclear TAI (or TAF) C*-algebra with UCT property. In [Jiang1], the second author classified all ATAI algebras by an invariant consisting orderd total K-theory and tracial state spaces of cut down algebras under an extra restriction that all element in K₁(A) are torsion. In this paper, we remove this restriction, and obtained the classification for all ATAI algebras with the Hausdorffized algebraic K₁-group as an addition to the invariant used in [Jiang1]. The theorem is proved by reducing the class to the classification theorem of AHD algebras with ideal property which is done in [GJL1]. Our theorem generalizes the main theorem of [Fa] and [Jiang1] (see corollary 4.3).

Citations

• A classification of inductive limit C^*-algebras with ideal property

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