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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| Format: | Journal |
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2020
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| 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 |
| Summary: | © 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. |
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