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Some Algebraic Structure in the Dual of a Compact Group

Published online by Cambridge University Press:  20 November 2018

Richard Iltis
Richard Iltis*
Affiliation:
University of Oregon, Eugene, Oregon; University of Toronto, Toronto, Ontario
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Throughout this paper, G will denote a compact (Hausdorff) topological group with identity e. When G is abelian, there is no difficulty in relating the group multiplication in G to the multiplication in the dual of G since characters are homomorphisms with respect to pointwise multiplication and pointwise multiplication of characters yields another character. However, in the non-abelian case, there are two multiplications associated with the dual of G: (1) representations are homomorphisms with respect to composition multiplication, and (2) the tensor product of representations yields another representation.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1499 - 1510
Copyright
Copyright © Canadian Mathematical Society 1968

Footnotes

Research for this paper was supported by the National Science Foundation of the United States and the National Research Council of Canada.

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