Journal of Lie Theory 34 (2024), No. 1, 017--040
Copyright Heldermann Verlag 2024
Decomposition of Enveloping Algebras of Simple Lie Algebras and their Related Polynomial Algebras
Rutwig Campoamor-Stursberg
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 rank-two simple Lie algebras is revisited and completed with the analysis of the exceptional Lie algebra G2.
Keywords: Enveloping algebras, decomposition, simple Lie algebras.
MSC: 16S30, 17B25, 17B35.
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