2022/09/29 by Adam Malinowski, Ludomir Newelski, Malinowski, Adam +1
Mathematics · Computer Science · #Advanced Topology and Set Theory #Advanced Algebra and Logic #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2209.14838
Assume G\prec H are groups and \cal A⊆\cal P(G), \cal B⊆\cal P(H) are algebras of sets closed under left group translation. Under some additional assumptions we find algebraic connections between the Ellis [semi]groups of the G-flow S(\cal A) and the H-flow S(\cal B). We apply these results in the model theoretic context. Namely, assume G is a group definable in a model M and M\prec^* N. Using weak heirs and weak coheirs we point out some algebraic connections between the Ellis semigroups Sext,G(M) and Sext,G(N). Assuming every minimal left ideal in Sext,G(N) is a group we prove that the Ellis groups of Sext,G(M) are isomorphic to closed subgroups of the Ellis groups of Sext,G(N).