Weights of semi-invariants of the quotient division ring of an enveloping algebra

Abstract

Let L be a finite dimensional Lie algebra over a field k of characteristic zero, D(L) the quotient division ring of U(L). It is shown that the weights of the semi-invariants of D(L) form a finitely generated, free abelian group Arj(L). It follows, among other things, that the semicenter of D(L) is isomorphic to the group algebra of S.d{L) over the center Z(D(L)) of D(L).