Novikov algebras and Novikov structures on Lie algebras
Dietrich Burde, Karel Dekimpe, Kim Vercammen
TL;DR
This paper investigates the existence of Novikov structures on various classes of Lie algebras, providing new examples and counterexamples, and exploring conditions under which such structures exist.
Contribution
It presents the first example of a three-step nilpotent Lie algebra without a Novikov structure and shows that free three-step nilpotent Lie algebras do admit such structures.
Findings
A three-step nilpotent Lie algebra can lack a Novikov structure.
Free three-step nilpotent Lie algebras admit Novikov structures.
Certain high solvability class Lie algebras also admit Novikov structures.
Abstract
We study ideals of Novikov algebras and Novikov structures on finite-dimensional Lie algebras. We present the first example of a three-step nilpotent Lie algebra which does not admit a Novikov structure. On the other hand we show that any free three-step nilpotent Lie algebra admits a Novikov structure. We study the existence question also for Lie algebras of triangular matrices. Finally we show that there are families of Lie algebras of arbitrary high solvability class which admit Novikov structures.
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 · Algebraic structures and combinatorial models · Rings, Modules, and Algebras