8 citations · 11 across the 7 of their papers we have counts for
7 papers
On Dixmier's fourth problem
Alfons I. Ooms
Let L be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. Denote by U(L) its enveloping algebra with quotient division ring D(L). In 19…
The maximal abelian dimension of a Lie algebra, Rentschler's property and Milovanov's conjecture
Alfons I. Ooms
A finite dimensional Lie algebra L with magic number c(L) is said to satisfy Rentschler's property if it admits an abelian Lie subalgebra H of dimension at least c(L) - 1. We study…
The polynomiality of the Poisson center and semi-center of a Lie algebra and Dixmier's fourth problem
Alfons I. Ooms
Let L be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. We provide necessary and also some sufficient conditions in order for its Poi…
The Poisson center and polynomial, maximal Poisson commutative subalgebras, especially for nilpotent Lie algebras of dimension at most seven
Alfons I. Ooms
Let g be a finite dimensional Lie algebra over an algebraically closed field k of characteristic zero. We collect some general results on the Poisson center of S(g), including some…
Computing invariants and semi-invariants by means of Frobenius Lie algebras
Alfons I. Ooms
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 conditi…
A degree inequality for Lie algebras with a regular Poisson semi-center
A. I. Ooms, M. Van den Bergh
For Lie algebras whose Poisson semi-center is a polynomial ring we give a bound for the sum of the degrees of the generating semi-invariants. This bound was previously known in man…