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Definable topological dynamics and real Lie groups
Author(s) -
Jagiella Grzegorz
Publication year - 2015
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201400033
Subject(s) - mathematics , counterexample , abelian group , sort , group (periodic table) , topological dynamics , torsion (gastropod) , pure mathematics , discrete mathematics , combinatorics , arithmetic , medicine , biochemistry , chemistry , topological tensor product , organic chemistry , surgery , functional analysis , gene
We investigate definable topological dynamics of groups definable in an o‐minimal expansion of the field of reals. Assuming that a definable group G admits a model‐theoretic analogue of Iwasawa decomposition, namely the compact‐torsion‐free decomposition G = K H , we give a description of minimal subflows and the Ellis group of its universal definable flowS G ( R )in terms of this decomposition. In particular, the Ellis group of this flow is isomorphic toN G ( H ) ∩ K ( R ) . This provides a range of counterexamples to a question by Newelski whether the Ellis group is isomorphic to G / G 00 . We further extend the results to universal topological covers of definable groups, interpreted in a two‐sorted structure containing the o‐minimal sort R and a sort for an abelian group.