Journal of Lie Theory

no. 1
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, 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

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, Volume 34 (2024) no. 1, pp. 17-40. doi: 10.5802/jolt.1325
@article{JOLT_2024_34_1_a1,
     author = {Rutwig Campoamor-Stursberg and Ian 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/}
}
TY  - JOUR
AU  - Rutwig Campoamor-Stursberg
AU  - Ian Marquette
TI  - Decomposition of Enveloping Algebras of Simple Lie Algebras and their Related Polynomial Algebras
JO  - Journal of Lie Theory
PY  - 2024
SP  - 17
EP  - 40
VL  - 34
IS  - 1
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1325/
DO  - 10.5802/jolt.1325
ID  - JOLT_2024_34_1_a1
ER  - 
%0 Journal Article
%A Rutwig Campoamor-Stursberg
%A Ian Marquette
%T Decomposition of Enveloping Algebras of Simple Lie Algebras and their Related Polynomial Algebras
%J Journal of Lie Theory
%D 2024
%P 17-40
%V 34
%N 1
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1325/
%R 10.5802/jolt.1325
%F JOLT_2024_34_1_a1

Cited by Sources: