2017/02/03 by Guihua Gong, Gong, Guihua, Huaxin Lin +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1702.01073
openalex publication_date 2017/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a classification theorem for amenable simple stably projectionless C*-algebras with generalized tracial rank one whose K0 vanish on traces which satisfy the Universal Coefficient Theorem. One of them is denoted by \cal Z0 which has a unique tracial state and K0(\cal Z0)=ℤ and K1(\cal Z0)=\0\. Let A and B be two separable simple C^*-algebras satisfying the UCT and have finite nuclear dimension. We show that A⊗ \cal Z0≅ B⊗ \cal Z0 if and only if \rm Ell(B⊗ \cal Z0)=\rm Ell(B⊗ \cal Z0). A class of simple separable C^*-algebras which are approximately sub-homogeneous whose spectra having bounded dimension is shown to exhaust all possible Elliott invariant for C^*-algebras of the form A⊗ \cal Z0, where A is any finite separable simple amenable C^*-algebras. Suppose that A and B are two finite separable simple C^*-algebras with finite nuclear dimension satisfying the UCT such that traces vanishe on K0(A) and K0(B) (but arbitrary K1). One consequence of the main results in this situation is that A≅ B if and only if A and B have the isomorphic Elliott invariant.