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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Kernels of representations and group extensions


Author: I. Schochetman
Journal: Proc. Amer. Math. Soc. 36 (1972), 564-570
MSC: Primary 22D10
MathSciNet review: 0320222
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Abstract: We first determine the kernels of those unitary representations of a locally compact group which are obtained by integrating, inducing and tensoring. We then describe a broad class of group extensions for which the previous results can be used to find (1) the kernel of any representation and (2) necessary and sufficient conditions for these extensions to be maximally almost periodic.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0320222-0
Keywords: Locally compact group, unitary representation, kernel of a representation, direct integral representation, induced representation, tensor product representation, projective representation, group extension, central extension, maximally almost periodic
Article copyright: © Copyright 1972 American Mathematical Society