The index of nilpotent Lie algebras

2025/05/13 by Burde, Dietrich, Dekimpe, Karel
#17B08 #17B30 #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2505.08331

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.

Citations

• Characteristically nilpotent Lie groups with flat coadjoint orbits
• The maximal abelian dimension of a Lie algebra, Rentschler's property\n and Milovanov's conjecture
• Abelian ideals of maximal dimension for solvable Lie algebras
• The index of a Lie algebra, the centraliser of a nilpotent element, and the normaliser of the centraliser

Related

• On index of certain nilpotent Lie algebras
• The index of nilpotent Lie poset algebras
• The index of a Lie algebra, the centraliser of a nilpotent element, and the normaliser of the centraliser
• On the index of certain Lie algebras
• Index of Graded Filiform and Quasi Filiform Lie Algebras