Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups

• Date: 2018
• Main Authors: Sushchansky, Vitaly I., Netreba, Nataliya V.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Lie algebra; wreath product; semidirect product; Lie algebra associated with the lower central series of the group; Sylow p-subgroup; symmetric group; 17B30; 17B60; 20F18; 20F40
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/921
• Journal Title: Algebra and Discrete Mathematics

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...