2021/09/02 by Sayan Chakraborty, Chakraborty, Sayan, Jiajie Hua +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2109.00739
openalex publication_date 2021/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Θ=(θjk)n× n be a real skew-symmetric n× n matrix for n≥ 2. Under some mild non-integrality conditions on Θ, we construct Rieffel-type projections as higher dimensional Bott classes in the n-dimensional noncommutative torus AΘ. These projections generate K0(AΘ) when Θ is strongly totally irrational. As an application, when Θ is strongly totally irrational, we show that: For any ε>0, there exists δ>0 (depending only on ε and Θ) satisfying the following: For any unital simple separable C^*-algebra A with tracial rank at most one, and for any n-tuple of unitaries u1,u2,…,un in A, if u1,u2,…,un satisfy certain trace conditions and \begineqnarray*‖ukuj-e^2πiθjkujuk‖