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Let L be a finite dimensional Lie algebra over a field k of char- acteristic 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). Introduction. Throughout this paper L will be a nonzero finite-dimensional Lie algebra over a field fc of characteristic zero. Let U(L) be the universal enveloping algebra of L with center Z(U(L)), D(L) the division ring of quotients of U(D with center Z(D(L)). For each X € L* we denote by D(L)X the set of those u G D(L) such that adx(u) — X(x)u for all x € L. Its elements are called the semi-invariants of D(L) relative to A.

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