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

Nauwelaerts, E.; Ooms, A. I.

doi:10.1090/S0002-9939-1988-0958034-9

Weights of semi-invariants of the quotient division ring of an enveloping algebra
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by E. Nauwelaerts and A. I. Ooms

Proc. Amer. Math. Soc. 104 (1988), 13-19

DOI: https://doi.org/10.1090/S0002-9939-1988-0958034-9

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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 ${\Lambda _D}(L)$. It follows, among other things, that the semicenter of $D(L)$ is isomorphic to the group algebra of ${\Lambda _D}(L)$ over the center $Z(D(L))$ of $D(L)$.

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