Abstract
AbstractIn the class of rank-1 transformations, there is a strong dichotomy. For such a T, the commutant is either irivial, consisting only of the powers of T, or is uncountable. In addition, the commutant semigroup, C(T), is in fact a group. As a consequence, the notion of weak isomorphism between two transformations is equivalent to isomorphism, if at least one of the transformations is rank-1. In § 2, we show that any proper factor of a rank-1 must be rigid. Hence, neither Ornstein's rank-1 mixing nor Chacón's transformation, can be a factor of a rank-1.
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