Purely Infinite Simple C* -Crossed Products II

Source abstract

Abstract We study the pure infiniteness of C * -crossed products by endomorphisms and automorphisms. Let A be a purely infinité simple unital C *-algebra. At first we show that a crossed product A × p N by a corner endomorphism p is purely infinite if it is simple. From this observation we prove that any simple C *-crossed products A × α Z by an automorphism α is purely infinite. Combining this with the result in [Je] on pure infiniteness of crossed products by finite groups, one sees that if α is an outer action by a countable abelian group G then the simple C *-algebra A × α G is purely infinite.