We study relationships between sequence entropy and the Kronecker and rigid algebras. Let (Y,y,v,T) be a factor of a measure-theoretical dynamical system (X, X, μ, T) and S be a sequence of positive integers with positive upper density. We prove there exists a subsequence ACS such that hA μ(T,ε | y) = Hμ(ε | K.(X | Y)) for all finite partitions ε, where K.(X | Y) is the Kronecker algebra over y. A similar result holds for rigid algebras over y. As an application, we characterize compact, rigid and mixing extensions via relative sequence entropy.
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