Extension of Maschke's theorem
| Autor: | Teerapong Suksumran |
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| Rok vydání: | 2018 |
| Předmět: | |
| DOI: | 10.48550/arxiv.1802.06680 |
| Popis: | In the present article, we examine linear representations of finite gyrogroups, following their group-counterparts. In particular, we prove the celebrated theorem of Maschke for gyrogroups, along with its converse. This suggests studying the left regular action of a gyrogroup $(G, \oplus)$ on the function space $$ L^{\mathrm{gyr}}(G) = \{f\in L(G)\colon \forall a, x, y, z\in G, f(a\oplus\mathrm{gyr}[x, y]z) = f(a\oplus z)\} $$ in a natural way, where $L(G)$ is the space of all functions from $G$ into a field. Comment: 17 pages |
| Databáze: | OpenAIRE |
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