Stability for biparabolic subalgebras of simple Lie algebras
arXiv:1808.04019
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.
in French. arXiv admin note: text overlap with arXiv:1305.1518; text overlap with arXiv:math/0503019 by other authors