Free nilpotent and nilpotent quadratic Lie algebras
Pilar Benito, Daniel de-la-Concepci\'on, Jes\'us Laliena

TL;DR
This paper establishes an equivalence between categories of t-nilpotent quadratic Lie algebras and symmetric invariant bilinear forms, leading to classifications for specific cases over fields of characteristic zero.
Contribution
It introduces a new categorical equivalence and classifies t-nilpotent quadratic Lie algebras with d generators for certain parameters.
Findings
Classification of t-nilpotent quadratic Lie algebras for d=2, t<6
Classification for d=3, t<4
Establishment of categorical equivalence
Abstract
In this paper we introduce an equivalence between the category of the t-nilpotent quadratic Lie algebras with d generators and the category of some symmetric invariant bilinear forms on the t-nilpotent free Lie algebra with d generators. Taking into account this equivalence, t-nilpotent quadratic Lie algebras with d generators are classified (up to isometric isomorphism, and over any field of characteristic zero), in the following cases: d=2 and t<6, d=3 and t<4.
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.
