Central polynomials for adjoint representations of simple Lie algebras exist
Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1015-1025
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Yu. P. Razmyslov has proved that for any finite dimensional reductive Lie algebra $\mathcal G$ over a field $K$ of zero characteristic ($\dim_{K}\mathcal G=m$) and for its arbitrary associative enveloping algebra $U$ with non-empty center $Z(U)$ there exists a central polynomial which is multilinear and skew-symmetric in $k$ sets of $m$ variables for a certain positive integer $k$. This result is now proved for adjoint representations of classical simple Lie algebras of type $A_s,B_s,C_s,D_s$ and matrix Lie algebra $M_n$ over fields of positive characteristic.
@article{FPM_1999_5_4_a4,
author = {A. A. Kagarmanov and Yu. P. Razmyslov},
title = {Central polynomials for adjoint representations of simple {Lie} algebras exist},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {1015--1025},
publisher = {mathdoc},
volume = {5},
number = {4},
year = {1999},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a4/}
}
TY - JOUR AU - A. A. Kagarmanov AU - Yu. P. Razmyslov TI - Central polynomials for adjoint representations of simple Lie algebras exist JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 1999 SP - 1015 EP - 1025 VL - 5 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a4/ LA - ru ID - FPM_1999_5_4_a4 ER -
%0 Journal Article %A A. A. Kagarmanov %A Yu. P. Razmyslov %T Central polynomials for adjoint representations of simple Lie algebras exist %J Fundamentalʹnaâ i prikladnaâ matematika %D 1999 %P 1015-1025 %V 5 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a4/ %G ru %F FPM_1999_5_4_a4
A. A. Kagarmanov; Yu. P. Razmyslov. Central polynomials for adjoint representations of simple Lie algebras exist. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1015-1025. http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a4/