(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 4, PAGES 1015-1025

## Central polynomials for adjoint representations of simple Lie algebras exist

A. A. Kagarmanov
Yu. P. Razmyslov

Abstract

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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 ($\dim _\left\{K\right\} \mathcal G = m$) and for its arbitrary associative enveloping algebra $U$ with non-empty center $Z\left(U\right)$ 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,Bs,Cs,Ds and matrix Lie algebra $M$n over fields of positive characteristic.

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