Zwei Klassen lokalkompakter maximal fastperiodischer Gruppen |
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Authors: | Dr Detlev Poguntke |
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Institution: | (1) Fakultät für Mathematik, Universität Bielefeld, Kurt-Schumacher-Straße 6, Postfach 8640, D-4800 Bielefeld, Bundesrepublik Deutschland |
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Abstract: | In this paper we study the class
of all locally compact groupsG with the property that for each closed subgroupH ofG there exists a pair of homomorphisms into a compact group withH as coincidence set, and the class
of all locally compact groupG with the property that finite dimensional unitary representations of subgroups ofG can be extended to finite dimensional representations ofG. It is shown that MOORE]-groups (every irreducible unitary representation is finite dimensional) have these two properties. A solvable group in
is a MOORE]-group. Moreover, we prove a structure theorem for Lie groups in the class MOORE], and show that compactly generated Lie groups in MOORE] have faithful finite dimensional unitary representations. |
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Keywords: | |
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