PERMANENCE OF NUCLEAR DIMENSION FOR INCLUSIONS OF UNITAL C*-ALGEBRAS WITH THE ROKHLIN PROPERTY

Let P subset of A be an inclusion of unital C*-algebras and E: A -> P be a faithful conditional expectation of index finite type. Suppose that E has the Rokhlin property. Then dr(P) <= dr(A) and dim(nuc)(P) <= dim(nuc)(A). This can be applied to Rokhlin actions of finite groups. We also show that under the same above assumption if A is exact and pure, that is, the Cuntz semigroups W(A) has strict comparison and is almost divisible, then P and the basic contruction C* < A, e(P)> are also pure.