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arXiv · 2505.08331

The index of nilpotent Lie algebras

Dietrich Burde·Karel Dekimpe
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Abstract

The index of a Lie algebra is an important invariant which arises in several areas, e.g. in the study of coadjoint orbits for a Lie group, in invariant theory and in representation theory. We study the index for several classes of nilpotent Lie algebras. In particular, we give explicit formulas for free-nilpotent Lie algebras of nilpotency class two and three, or of solvability class two, for graph Lie algebras, and for filiform nilpotent Lie algebras.

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Dietrich Burde, Karel Dekimpe. 2025-05-13. The index of nilpotent Lie algebras. https://arxiv.org/abs/2505.08331

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