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Enveloping semigroups of systems of order d

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  • In this paper we study the Ellis semigroup of a $d$-step nilsystem and the inverse limit of such systems. By using the machinery of cubes developed by Host, Kra and Maass, we prove that such a system has a $d$-step topologically nilpotent enveloping semigroup. In the case $d=2$, we prove that these notions are equivalent, extending a previous result by Glasner.
    Mathematics Subject Classification: Primary: 37B05, 37B99.

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