Computing invariants and semi-invariants by means of Frobenius Lie algebras

Details Computing invariants and semi-invariants by means of Frobenius Lie algebras Computing invariants and semi-invariants by means of Frobenius Lie algebras

2008-06-25

arxiv.org/abs/0806.4178v1

Mathematics

Representation Theory

35 pages

Scientific paper

Let U(L) be the enveloping algebra of a finite dimensional Lie algebra L over a field k of characteristic zero, Z(U(L)) its center and Sz(U(L)) its semicenter. A sufficient condition is given in order for Sz(U(L)) to be a polynomial algebra over k. Surprisingly, this condition holds for many Lie algebras, especially among those for which the radical is nilpotent, in which case Sz(U(L))=Z(U(L)). In particular, it allows the explicit description of Z(U(L)) for more than half of all complex, indecomposable nilpotent Lie algebras of dimension at most 7.

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