Kais Ammari
Published 2018-08-12Version 1
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.
Comments: in French. arXiv admin note: text overlap with arXiv:1305.1518; text overlap with arXiv:math/0503019 by other authors
Simple prolongs of the non-positive parts of graded Lie algebras with Cartan matrix in characteristic 2
Short $SL_2$-structures on simple Lie algebras
Structure constants for simple Lie algebras from principal $\mathfrak{sl}_2$-triple
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