Index and stable linear forms of Lie algebras

2003/02/05 by Patrice Tauvel, Rupert W. T. Yu
Mathematics · #math.RT #msc:17B45 #msc:17B20

paper · pdf · doi:10.1016/s0021-8693(03)00376-4

published as Journal of Algebra 273 (2004) 507-516 · This paper is written in French

arxiv created 2003/02/05 · arxiv updated 2009/11/30

Abstract

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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