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
Hauptverfasser: Sushchansky, Vitaly I., Netreba, Nataliya V.
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2018
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Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/921
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
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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.