A rank-one, rigid, simple, prime map

Abstract

AbstractWe construct a rank-1 mapTsimilar to Chacon's map [C], [JRS], but with 2n+1n-blocks in an (n + 1)-block and a single spacer in the middle. HenceTis rigid and the centralizer ofT, C(T), is uncountable. We showTis simple [V], [JR], and hence any factor ofTis the algebra of invariant sets of some weakly compact subgroup ofC(T). We showC(T) has no such subgroups and henceTis prime. Lastly we show thatTis graphic in the sense of [AM].