Herbert Heyer, Satoshi Kawakami, Tatsuya Tsurii, Satoe Yamanaka, “Hypergroups Related to a Pair of Compact Hypergroups”, SIGMA, 2016, Volume 12,111, 17 pp.

This article is cited in 1 paper

Hypergroups Related to a Pair of Compact Hypergroups

Herbert Heyer^a, Satoshi Kawakami^b, Tatsuya Tsurii^c, 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

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.

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

MSC: 22D30; 22F50; 20N20; 43A62

Received: June 2, 2016; in final form November 10, 2016; Published online November 18, 2016

Language: English

DOI: 10.3842/SIGMA.2016.111