Classification of Novikov algebras
Dietrich Burde, Willem A. de Graaf

TL;DR
This paper develops a classification method for Novikov algebras based on their associated Lie algebras and applies it to classify 3-dimensional Novikov algebras over R and C, and certain 4-dimensional cases over C.
Contribution
It introduces a new classification approach for Novikov algebras and provides comprehensive classifications for specific low-dimensional cases.
Findings
Classified all 3-dimensional Novikov algebras over R and C.
Classified 4-dimensional Novikov algebras over C with nilpotent associated Lie algebra.
Included a list of all 4-dimensional commutative associative algebras over C.
Abstract
We describe a method for classifying the Novikov algebras with a given associated Lie algebra. Subsequently we give the classification of the Novikov algebras of dimension 3 over R and C, as well as the classification of the 4-dimensional Novikov algebras over C whose associated Lie algebra is nilpotent. In particular this includes a list of all 4-dimensional commutative associative algebras over C.
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 · Advanced Operator Algebra Research
