Author： Bavula V. V.
Publisher： Taylor & Francis Ltd
ISSN： 0092-7872
Source： Communications in Algebra, Vol.36, Iss.6, 2008-06, pp. : 2195-2201
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Abstract
Let D be a division algebra such that D⊗ Do is a Noetherian algebra, and Δ be a set of derivations or automorphisms of the division algebra D, then the group Ev(Δ) of common eigenvalues (i.e., weights) is a finitely generated abelian group. Typical examples of D are the quotient division algebra Frac (D (X)) of the ring of differential operators D (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 .
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