2016/08/10 by Nathanial P. Brown, N. P. Brown, Brown, N. P. +6
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1608.03214
arxiv created 2016/08/10 · openalex publication_date 2016/08/10 · arxiv updated 2016/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the notion of Rokhlin dimension from topological dynamical systems to C^*-correspondences. We show that in the presence of finite Rokhlin dimension and a mild quasidiagonal-like condition (which, for example, is automatic for finitely generated projective correspondences), finite nuclear dimension passes from the scalar algebra to the associated Toeplitz--Pimsner and (hence) Cuntz--Pimsner algebras. As a consequence we provide new examples of classifiable C^*-algebras: if A is simple, unital, has finite nuclear dimension and satisfies the UCT, then for every finitely generated projective H with finite Rokhlin dimension, the associated Cuntz--Pimsner algebra O (H) is classifiable in the sense of Elliott's Program.