Journal of Lie Theory

no. 1
Decomposition of Enveloping Algebras of Simple Lie Algebras and their Related Polynomial Algebras
Journal of Lie Theory, Volume 34 (2024) no. 1, pp. 17-40
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.
DOI: 10.5802/jolt.1325
Classification: 16S30, 17B25, 17B35
Keywords: Enveloping algebras, decomposition, simple Lie algebras 
@article{JOLT_2024_34_1_a1,
     author = {R. Campoamor-Stursberg and I. Marquette},
     title = {Decomposition of {Enveloping} {Algebras} of {Simple} {Lie} {Algebras} and their {Related} {Polynomial} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {17--40},
     year = {2024},
     volume = {34},
     number = {1},
     doi = {10.5802/jolt.1325},
     zbl = {1542.16023},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1325/}
}
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R. Campoamor-Stursberg; I. Marquette. Decomposition of Enveloping Algebras of Simple Lie Algebras and their Related Polynomial Algebras. Journal of Lie Theory, Volume 34 (2024) no. 1, pp. 17-40. doi: 10.5802/jolt.1325

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