منابع مشابه
Remark on the Duality for Noncommutative Compact Groups
The duality theorem for noncommutative compact groups was established by Tannaka,1 and later, but independently, by Krein.2 Different proofs have been given by Bochner and Yosida.3 The purpose of the present note is to supplement the theorem by a duality between (closed) subgroups and certain representation-theoretically defined systems. It provides also an extension of Tannaka's theorem itself...
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15 صفحه اولDuality for Groups
If F is known to be free, with generators gi, /3 may be constructed by setting j3g; = &», with bi so chosen that pbi = agi. Conversely, let F have the cited property and represent F as a quotient group Fo/Ro> where F0 is a free abelian group. Choose A—F and B = Fo in (1.1), let a be the identity, and p the given homomorphism of .Fo onto F with kernel Ro. Then, by (1.2), a=p/3 is an isomorphism,...
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The well-known duality theorem of Pontryagin and van Kampen [27, 20] states that the characters of an Abelian locally compact group G also form a group Ĝ, and the group of characters of Ĝ is isomorphic to G. For non-Abelian groups, there is no such duality. In a few words, difficulties on this way arise from the fact that the dual space of a noncommutative group, however defined, has no natural...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1963
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.49.4.457