EXTENSIONS OF PONTRYAGIN HYPERGROUPS
Abstract: The purpose of this paper is to investigate the extension problem for the category of
commutative hypergroups. In fact, by applying the new notion of a field of compact
subhypergroups, sufficiently many extensions can be established, and among them splitting
extensions can be characterized. Moreover, the duality of extensions will be studied via
duality of fields of hypergroups. The method of extension via fields of hypergroups yields the
construction of Pontryagin hypergroups which do not arise from group-theoretic objects.
2000 AMS Mathematics Subject Classification: 43A62.
Key words and phrases: Hypergroups, extensions, duality.