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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: E. Nauwelaerts and A. I. Ooms
Journal: Proc. Amer. Math. Soc. 104 (1988), 13-19
MSC: Primary 17B35; Secondary 16A33, 16A39
MathSciNet review: 958034
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0958034-9
PII: S 0002-9939(1988)0958034-9
Keywords: Finite-dimensional Lie algebra, universal enveloping algebra, semi-invariants
Article copyright: © Copyright 1988 American Mathematical Society