Meander graphs and Frobenius Seaweed Lie algebras

TL;DR

This paper explores meander graphs associated with seaweed Lie algebras to identify new families of Frobenius algebras with zero index, providing both novel results and simplified proofs of known cases.

Contribution

It introduces two new families of Frobenius seaweed Lie algebras and offers elementary proofs for existing families, advancing understanding of their structure.

Findings

Identified two new families of Frobenius seaweed Lie algebras

Provided elementary proofs for known Frobenius families

Enhanced methods for analyzing meander graphs in Lie algebra classification

Abstract

The index of a seaweed Lie algebra can be computed from its associated meander graph. We examine this graph in several ways with a goal of determining families of Frobenius (index zero) seaweed algebras. Our analysis gives two new families of Frobenius seaweed algebras as well as elementary proofs of known families of such Lie algebras.