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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| Format: | Journal |
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2020
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| Online Access: | 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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| Institution: | Chiang Mai University |
| Summary: | © 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]. |
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