Nuclear dimension for an inclusion of unital C*-algebras

2011/11/08 by Hiroyuki Osaka, Osaka, Hiroyuki, Tamotsu Teruya +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.OA #msc:46L35 #msc:46L55

paper · pdf · doi:10.48550/arxiv.1111.1808

16 pages

arxiv created 2011/11/08 · arxiv updated 2011/11/09

Abstract

Let P ⊂ A be an inclusion of separable unital C*-algebras with finite Watatani index. Suppose that E \colon A → P has the Rokhlin property, that is, there is a projection e ∈ A' ∩ A^∞ such that E^∞(e) = (\rm IndexE)^-11. We show that if A has nuclear dimension n, then P has nuclear dimension less than or equal to n. In particular, if an action α of a finite group G on A has the Rokhlin property, then the nuclear dimension of the crossed product algebra A \rtimes_αG is less than or equal to that of A.

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