The index of nilpotent Lie algebras
Representation Theory
2025-05-14 v1 Rings and Algebras
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.
Keywords
Cite
@article{arxiv.2505.08331,
title = {The index of nilpotent Lie algebras},
author = {Dietrich Burde and Karel Dekimpe},
journal= {arXiv preprint arXiv:2505.08331},
year = {2025}
}