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DUAL SPACE AND HYPERDIMENSION OF COMPACT HYPERGROUPS

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  10 June 2016

MAHMOOD ALAGHMANDAN  and
MASSOUD AMINI
MAHMOOD ALAGHMANDAN
Affiliation:
Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg SE-412 96, Sweden e-mail: [email protected]
MASSOUD AMINI
Affiliation:
Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran e-mail: [email protected]
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Abstract

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We characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite hypergroups. Also, studying the representation theory of finite hypergroups, we highlight some interesting differences and similarities between the representation theories of finite hypergroups and finite groups. Finally, we compute the Heisenberg inequality for compact hypergroups.

MSC classification

Primary: 43A62: Hypergroups
Secondary: 43A40: Character groups and dual objects 43A65: Representations of groups, semigroups, etc.
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 2 , May 2017 , pp. 421 - 435
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

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