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Journal of Lie Theory 32 (2022), No. 1, 239--260
Copyright Heldermann Verlag 2022

Stabilité des Sous-Algèbres Biparaboliques des Algèbres de Lie Simples

Kais Ammari
Département de Mathématiques, Faculté des Sciences, Université Tunis El-Manar, Tunisia

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].

Keywords: Simple Lie algebras, root systems, coadjoint action, stable Lie algebra, quasi-reductive Lie algebra, stable linear form, strongly regular linear form.

MSC: 17B45, 17B20, 17 B22, 22E60.

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