Geodesic
Decomposition of Enveloping Algebras of Simple Lie Algebras and their Related Polynomial Algebras
Rutwig Campoamor-Stursberg1 ; Ian Marquette2
1Instituto de Matemática Interdisciplinar, Dpto. Geometria y Topologia, Universidad Complutense, Madrid, Spain
2School of Mathematics and Physics, University of Queensland, Brisbane, Australia
Journal of Lie Theory, Tome 34 (2024) no. 1, pp. 17-40

Voir la notice de l'article provenant de la source Heldermann Verlag

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 rank-two simple Lie algebras is revisited and completed with the analysis of the exceptional Lie algebra G2.
Classification : 16S30, 17B25, 17B35
Mots-clés : Enveloping algebras, decomposition, simple Lie algebras

Rutwig Campoamor-Stursberg  1   ; Ian Marquette  2

1 Instituto de Matemática Interdisciplinar, Dpto. Geometria y Topologia, Universidad Complutense, Madrid, Spain
2 School of Mathematics and Physics, University of Queensland, Brisbane, Australia 
Rutwig Campoamor-Stursberg; Ian Marquette. Decomposition of Enveloping Algebras of Simple Lie Algebras and their Related Polynomial Algebras. Journal of Lie Theory, Tome 34 (2024) no. 1, pp. 17-40. http://geodesic.mathdoc.fr/item/JOLT_2024_34_1_a1/
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