CENTRAL POLYNOMIALS IN IRREDUCIBLE REPRESENTATIONS OF A SEMISIMPLE LIE ALGEBRA

A central multilinear polynomial is constructed for every reductive finite-dimensional Lie algebra over an algebraically closed field of characteristic zero, and almost every faithful irreducible -representation of in a vector space . The central polynomial is of the form , where and is skew-symmetric with respect to the variables of each set (). The dimension of the vector space need not be finite.This result implies that, for the Lie algebra of all regular tangent vector fields of an -dimensional affine algebraic variety, one can construct an associative multilinear polynomial such that the map is a map onto the center of the algebra , which is isomorphic to the algebra of all regular functions of this variety.Bibliography: 10 titles.