FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(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 $\$\; \backslash mathcal\; G\; \$$ over a field $K$ of zero characteristic ($\$\; \backslash dim\; \_\{K\}\; \backslash mathcal\; G\; =\; m\; \$$) 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.

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Last modified: December 9, 1999