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arXiv · 2204.11395

Decomposition of enveloping algebras of simple Lie algebras and their related polynomial algebras

Rutwig Campoamor-Stursberg·Ian Marquette
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Abstract

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 decomposition problem for the exceptional Lie algebra $G_2$ is completely solved.

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Rutwig Campoamor-Stursberg, Ian Marquette. 2022-04-25. Decomposition of enveloping algebras of simple Lie algebras and their related polynomial algebras. https://arxiv.org/abs/2204.11395

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