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arXiv · 1808.04019

Stability for biparabolic subalgebras of simple Lie algebras

Kais Ammari
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Abstract

Let K be an algebraically closed field of characteristic 0. It is well known that any quasi-reductive Lie algebra is stable. However, there are stable Lie algebras which are not quasi-reductive. This raises the question, if for some particular class of non-reductive Lie algebras, there is equivalence between stability and quasi-reductivity. In particular, it was conjectured by Panyushev that these two notions are equivalent for biparabolic subalgebras of a reductive Lie algebra. In this paper, we give a positive answer to this conjecture.

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Kais Ammari. 2018-08-12. Stability for biparabolic subalgebras of simple Lie algebras. https://arxiv.org/abs/1808.04019

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