Abstract
Let U ( ▪ ) be the enveloping algebra of a finite-dimensional Lie algebra ▪ over a field k of characteristic zero, Z ( U ( ▪ ) ) its center and Sz ( U ( ▪ ) ) its semi-center. A sufficient condition is given in order for Sz ( U ( ▪ ) ) 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 ( ▪ ) ) = Z ( U ( ▪ ) ) . In particular, it allows the explicit description of Z ( U ( ▪ ) ) for more than half of all complex, indecomposable nilpotent Lie algebras of dimension at most 7.
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