Left regular representation of gyrogroups
© 2019 by the authors. In this article, we examine a subspace Lgyr(G) of the complex vector space, L(G) = [f: f is a function from G to C], where G is a nonassociative group-like structure called a gyrogroup. The space Lgyr(G) arises as a representation space for G associated with the left regular r...
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th-cmuir.6653943832-684602020-04-02T15:27:41Z Left regular representation of gyrogroups Teerapong Suksumran Mathematics © 2019 by the authors. In this article, we examine a subspace Lgyr(G) of the complex vector space, L(G) = [f: f is a function from G to C], where G is a nonassociative group-like structure called a gyrogroup. The space Lgyr(G) arises as a representation space for G associated with the left regular representation, consisting of complex-valued functions invariant under certain permutations of G. In the case when G is finite, we prove that dim (where γ(G) is the sub group of Sym (G) generated by a class of permutations of G and Fix (ρ) = [a ∈ G: ρ(a) = a]. 2020-04-02T15:27:41Z 2020-04-02T15:27:41Z 2020-01-01 Journal 22277390 2-s2.0-85079660333 10.3390/MATH8010012 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85079660333&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/68460 |
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Mathematics Teerapong Suksumran Left regular representation of gyrogroups |
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© 2019 by the authors. In this article, we examine a subspace Lgyr(G) of the complex vector space, L(G) = [f: f is a function from G to C], where G is a nonassociative group-like structure called a gyrogroup. The space Lgyr(G) arises as a representation space for G associated with the left regular representation, consisting of complex-valued functions invariant under certain permutations of G. In the case when G is finite, we prove that dim (where γ(G) is the sub group of Sym (G) generated by a class of permutations of G and Fix (ρ) = [a ∈ G: ρ(a) = a]. |
| format |
Journal |
| author |
Teerapong Suksumran |
| author_facet |
Teerapong Suksumran |
| author_sort |
Teerapong Suksumran |
| title |
Left regular representation of gyrogroups |
| title_short |
Left regular representation of gyrogroups |
| title_full |
Left regular representation of gyrogroups |
| title_fullStr |
Left regular representation of gyrogroups |
| title_full_unstemmed |
Left regular representation of gyrogroups |
| title_sort |
left regular representation of gyrogroups |
| publishDate |
2020 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85079660333&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/68460 |
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