Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups
Algebra and discrete mathematics, no. 1 (2005), pp. 122-132
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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.
Keywords:
Lie algebra, wreath product, semidirect product, Lie algebra associated with the lower central series of the group, Sylow p-subgroup, symmetric group.
@article{ADM_2005_1_a10,
author = {Vitaly I. Sushchansky and Nataliya V. Netreba},
title = {Wreath product of {Lie} algebras and {Lie} algebras associated with {Sylow} p-subgroups of finite symmetric groups},
journal = {Algebra and discrete mathematics},
pages = {122--132},
publisher = {mathdoc},
number = {1},
year = {2005},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ADM_2005_1_a10/}
}
TY - JOUR AU - Vitaly I. Sushchansky AU - Nataliya V. Netreba TI - Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups JO - Algebra and discrete mathematics PY - 2005 SP - 122 EP - 132 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ADM_2005_1_a10/ LA - en ID - ADM_2005_1_a10 ER -
%0 Journal Article %A Vitaly I. Sushchansky %A Nataliya V. Netreba %T Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups %J Algebra and discrete mathematics %D 2005 %P 122-132 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/ADM_2005_1_a10/ %G en %F ADM_2005_1_a10
Vitaly I. Sushchansky; Nataliya V. Netreba. Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of finite symmetric groups. Algebra and discrete mathematics, no. 1 (2005), pp. 122-132. http://geodesic.mathdoc.fr/item/ADM_2005_1_a10/