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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Groups with finite dimensional irreducible representations


Author: Calvin C. Moore
Journal: Trans. Amer. Math. Soc. 166 (1972), 401-410
MSC: Primary 22D10
MathSciNet review: 0302817
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Abstract: It will be shown that a locally compact group has a finite bound for the dimensions of its irreducible unitary representations if and only if it has a closed abelian subgroup of finite index. It will further be shown that a locally compact group has all of its irreducible representations of finite dimension if and only if it is a projective limit of Lie groups with the same property, and finally that a Lie group has this property if and only if it has a closed subgroup H of finite index such that H modulo its center is compact.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0302817-8
PII: S 0002-9947(1972)0302817-8
Article copyright: © Copyright 1972 American Mathematical Society