Seaweed algebras
Alex Cameron, Vincent E. Coll Jr, Nicholas Mayers, and Nicholas, Russoniello

TL;DR
This paper introduces seaweed algebras, explaining how their index can be computed using combinatorial methods involving meander graphs, making the process accessible to a broader audience.
Contribution
It provides a survey of seaweed algebras, including new results and a simplified combinatorial approach to computing their index, with minimal reliance on advanced Lie theory.
Findings
Index computation reduces to a combinatorial formula
Introduction of meander graphs for algebra analysis
New results on seaweed algebra properties
Abstract
The index of a Lie algebra is an important algebraic invariant, but it is notoriously difficult to compute. However, for the suggestively-named seaweed algebras, the computation of the index can be reduced to a combinatorial formula based on the connected components of a "meander": a planar graph associated with the algebra. Our index analysis on seaweed algebras requires only basic linear and abstract algebra. Indeed, the main goal of this survey-type article is to introduce a broader audience to seaweed algebras with minimal appeal to specialized language and notation from Lie theory. This said, we present several results that do not appear elsewhere and do appeal to more advanced language in the Introduction to provide added context.
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
TopicsLinguistics and Language Studies · Advanced Topics in Algebra
