Elements of a Lie algebra acting nilpotently in all its representations
O.G. Styrt
TL;DR
This paper characterizes elements of a Lie algebra that act nilpotently in all representations, showing they must belong to the derived algebra and map to nilpotent elements in the semisimple quotient.
Contribution
It provides an equivalent condition for nilpotent action in all representations, linking algebraic structure to representation theory.
Findings
Elements acting nilpotently in all representations belong to the derived algebra.
Such elements map to nilpotent elements in the semisimple quotient.
The paper establishes a criterion connecting algebraic properties with representation behavior.
Abstract
An equivalent condition for an element of a Lie algebra acting nilpotently in all its representations is obtained. Namely, it should belong to the derived algebra and go via factoring over the radical to a nilpotent element of the corresponding (semisimple) quotient algebra.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Finite Group Theory Research