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Realizations of rotations on an indecomposable compact monothetic group
Author(s) -
Maier Daniel
Publication year - 2015
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201400077
Subject(s) - mathematics , indecomposable module , ergodic theory , locally compact space , group (periodic table) , compact group , locally compact group , pure mathematics , measure (data warehouse) , product (mathematics) , topology (electrical circuits) , combinatorics , lie group , geometry , chemistry , organic chemistry , database , computer science
By the classical Halmos‐von Neumann theorem, each compact monothetic group corresponds to an ergodic dynamical system with discrete spectrum. For such groups we prove two results. We first construct a compact monothetic group which does not split into a direct product of a connected and a totally disconnected compact monothetic group. Then we present a measure preserving dynamical system on the unit square being isomorphic to a rotation on this indecomposable group.