Lie algebra representations, nilpotent matrices, and the C–numerical range

Lie Algebra Prederivations and Strongly Nilpotent Lie Algebras

We study Lie algebra prederivations. A Lie algebra admitting a non-singular prederivation is nilpotent. We classify filiform Lie algebras admitting a non-singular prederivation but no non-singular derivation. We prove that any 4-step nilpotent Lie algebra admits a non-singular prederivation.

Unitary Representations of Nilpotent Super Lie Groups

We prove that irreducible unitary representations of nilpotent super Lie groups can be obtained by induction from a distinguished class of sub super Lie groups which are natural generalizations of polarizing subgroups that appear in classical Kirillov theory. We prove that this kind of induction always yields irreducible unitary representations. We also prove a uniqueness result for the inducin...

Lie Algebra Cohomology and the Representations Ofsemisimple Lie Groups

Lie Representations and an Algebra Containing Solomon's

We introduce and study a Hopf algebra containing the descent algebra as a sub-Hopf-algebra. It has the main algebraic properties of the descent algebra, and more: it is a sub-Hopf-algebra of the direct sum of the symmetric group algebras; it is closed under the corresponding inner product; it is cocommutative, so it is an enveloping algebra; it contains all Lie idempotents of the symmetric grou...

A Note on the Representations of Nilpotent Lie Algebras1