Journal of Lie Theory

no. 1
Stabilité des Sous-Algèbres Biparaboliques des Algèbres de Lie Simples
Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 239-260
Let K be an algebraically closed commutative field of characteristic 0. We prove the equivalence between stability and quasi-reductivity for biparabolic subalgebras of reductive Lie algebras. Therefore, we give a positive answer to the assertion (ii) of the conjecture (5.6) of D. I. Panyushev [An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras, Ann. Inst. Fourier (Grenoble) 55 (2005) 693--715].
DOI: 10.5802/jolt.1228
Classification: 17B45, 17B20, 17 B22, 22E60
Keywords: Simple Lie algebras, root systems, coadjoint action, stable Lie algebra, quasi-reductive Lie algebra, stable linear form, strongly regular linear form 
@article{JOLT_2022_32_1_a11,
     author = {K. Ammari},
     title = {Stabilit\'e des {Sous-Alg\`ebres} {Biparaboliques} des {Alg\`ebres} de {Lie} {Simples}},
     journal = {Journal of Lie Theory},
     pages = {239--260},
     year = {2022},
     volume = {32},
     number = {1},
     doi = {10.5802/jolt.1228},
     zbl = {1486.17017},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1228/}
}
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K. Ammari. Stabilité des Sous-Algèbres Biparaboliques des Algèbres de Lie Simples. Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 239-260. doi: 10.5802/jolt.1228

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