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math.RT2025
The index of nilpotent Lie algebras
Dietrich Burde, Karel Dekimpe
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…
math.RT2025
Characteristically nilpotent Lie groups with flat coadjoint orbits
Dietrich Burde, Jordy Timo van Velthoven
We study the existence of certain characteristically nilpotent Lie algebras with flat coadjoint orbits. Their connected, simply connected Lie groups admit square-integrable represe…
math.RT2024
Cohomology of perfect Lie algebras
Dietrich Burde, Friedrich Wagemann
We study the adjoint cohomology of perfect Lie algebras over the complex numbers. For the family of perfect Lie algebras we obtain…