Index and stable linear forms of Lie algebras

Details Index and stable linear forms of Lie algebras Index and stable linear forms of Lie algebras

2003-02-05

arxiv.org/abs/math/0302048v1

Journal of Algebra 273 (2004) 507-516

Mathematics

Representation Theory

This paper is written in French

Scientific paper

10.1016/S0021-8693(03)00376-4

We characterize, in a purely algebraic manner, certain linear forms, called
stable, on a Lie algebra. As an application, we determine the index of a Borel
subalgebra of a semi-simple Lie algebra. Finally, we give an example of a
parabolic subalgebra of a semi-simple Lie algebra which does not admit any
stable linear form.

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