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

• Опубліковано в: : Algebra and Discrete Mathematics
• Дата: 2005
• Автори: Sushchansky, V.I., Netreba, N.V.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут прикладної математики і механіки НАН України 2005
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/156611
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups / V.I. Sushchansky, N.V. Netreba // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 1. — С. 122–132. — Бібліогр.: 11 назв. — англ.

We define a wreath product of a Lie algebra L
 with the one-dimensional Lie algebra L1 over Fp and determine
 some properties of this wreath product. We prove that the Lie
 algebra associated with the Sylow p-subgroup of finite symmetric
 group Spm is isomorphic to the wreath product of m copies of L1.
 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.