### Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 111, 17 pages      arXiv:1605.07010      https://doi.org/10.3842/SIGMA.2016.111

### Hypergroups Related to a Pair of Compact Hypergroups

Herbert Heyer a, Satoshi Kawakami b, Tatsuya Tsurii c and Satoe Yamanaka d
a) Universität Tübingen, Mathematisches Institut, Auf der Morgenstelle 10, 72076, Tübingen, Germany
b) Nara University of Education, Department of Mathematics, Takabatake-cho Nara, 630-8528, Japan
c) Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai Osaka, 599-8531, Japan
d) Nara Women's University, Faculty of Science, Kitauoya-higashimachi, Nara, 630-8506, Japan

Received June 02, 2016, in final form November 10, 2016; Published online November 18, 2016

Abstract
The purpose of the present paper is to investigate a hypergroup associated with irreducible characters of a compact hypergroup $H$ and a closed subhypergroup $H_0$ of $H$ with $|H/H_0|$<$+ \infty$. The convolution of this hypergroup is introduced by inducing irreducible characters of $H_0$ to $H$ and by restricting irreducible characters of $H$ to $H_0$. The method of proof relies on the notion of an induced character and an admissible hypergroup pair.

Key words: hypergroup; induced character; semi-direct product hypergroup; admissible hypergroup pair.

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