
Journal of Lie Theory 34 (2024), No. 1, 017040 Copyright Heldermann Verlag 2024 Decomposition of Enveloping Algebras of Simple Lie Algebras and their Related Polynomial Algebras Rutwig CampoamorStursberg Instituto de Matemática Interdisciplinar, Dpto. Geometria y Topologia, Universidad Complutense, Madrid, Spain rutwig@ucm.es Ian Marquette School of Mathematics and Physics, University of Queensland, Brisbane, Australia i.marquette@uq.edu.au The decomposition problem of the enveloping algebra of a simple Lie algebra is reconsidered combining both the analytical and the algebraic approach, showing its relation with the internal labelling problem with respect to a nilpotent subalgebra. A lower bound for the number of generators of the commutant as well as the maximal Abelian subalgebra are obtained. The case of ranktwo simple Lie algebras is revisited and completed with the analysis of the exceptional Lie algebra G_{2}. Keywords: Enveloping algebras, decomposition, simple Lie algebras. MSC: 16S30, 17B25, 17B35. [ Fulltextpdf (204 KB)] for subscribers only. 