Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups
We define a wreath product of a Lie algebra \(L\) with the one-dimensional Lie algebra \(L_1\) over \(\mathbb{F}_p\) and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of finite symmetric group \(S_{p^m}\) is isomorphic to the wre...
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| Datum: | 2018 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/921 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Zusammenfassung: | We define a wreath product of a Lie algebra \(L\) with the one-dimensional Lie algebra \(L_1\) over \(\mathbb{F}_p\) and determine some properties of this wreath product. We prove that the Lie algebra associated with the Sylow p-subgroup of finite symmetric group \(S_{p^m}\) is isomorphic to the wreath product of \(m\) copies of \(L_1\). As a corollary we describe the Lie algebra associated with Sylow p-subgroup of any symmetric group in terms of wreath product of one-dimensional Lie algebras. |
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