A rank-one, rigid, simple, prime map

Abstract

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