Complete reducibility of gyrogroup representations

© 2019, © 2019 Taylor & Francis Group, LLC. In this article, we show that any finite gyrogroup can be represented on a space of complex-valued functions. In particular, we prove that any linear representation of a finite gyrogroup on a finite-dimensional complex inner product space is unitary...

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Main Author:	Teerapong Suksumran
Format:	Journal
Published:	2020
Subjects:	Mathematics
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85073822408&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67915
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Institution:	Chiang Mai University

id	th-cmuir.6653943832-67915
record_format	dspace
spelling	th-cmuir.6653943832-679152020-04-02T15:11:16Z Complete reducibility of gyrogroup representations Teerapong Suksumran Mathematics © 2019, © 2019 Taylor & Francis Group, LLC. In this article, we show that any finite gyrogroup can be represented on a space of complex-valued functions. In particular, we prove that any linear representation of a finite gyrogroup on a finite-dimensional complex inner product space is unitary and hence is completely reducible using strong connections between linear actions of groups and gyrogroups. Also, we provide an example of a unitary representation of an arbitrary finite gyrogroup, which resembles the group-theoretic left regular representation. 2020-04-02T15:11:16Z 2020-04-02T15:11:16Z 2019-01-01 Journal 15324125 00927872 2-s2.0-85073822408 10.1080/00927872.2019.1662916 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85073822408&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67915
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Mathematics
spellingShingle	Mathematics Teerapong Suksumran Complete reducibility of gyrogroup representations
description	© 2019, © 2019 Taylor & Francis Group, LLC. In this article, we show that any finite gyrogroup can be represented on a space of complex-valued functions. In particular, we prove that any linear representation of a finite gyrogroup on a finite-dimensional complex inner product space is unitary and hence is completely reducible using strong connections between linear actions of groups and gyrogroups. Also, we provide an example of a unitary representation of an arbitrary finite gyrogroup, which resembles the group-theoretic left regular representation.
format	Journal
author	Teerapong Suksumran
author_facet	Teerapong Suksumran
author_sort	Teerapong Suksumran
title	Complete reducibility of gyrogroup representations
title_short	Complete reducibility of gyrogroup representations
title_full	Complete reducibility of gyrogroup representations
title_fullStr	Complete reducibility of gyrogroup representations
title_full_unstemmed	Complete reducibility of gyrogroup representations
title_sort	complete reducibility of gyrogroup representations
publishDate	2020
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85073822408&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67915
_version_	1681426723426533376

Complete reducibility of gyrogroup representations

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