Let D be a division algebra such that D ⊗ D o is a Noetherian algebra, and be a set of derivations or automorphisms of the division algebra D, then the group Ev of common eigenvalues (i.e., weights) is a finitely generated abelian group. Typical examples of D are the quotient division algebra Frac X of the ring of differential operators X on a smooth irreducible affine variety X over a field K of characteristic zero, and the quotient division algebra Frac U of the universal enveloping algebra U of a finite dimensional Lie algebra .