Families of Frobenius seaweed Lie algebras

TL;DR

This paper introduces new infinite families of Frobenius seaweed Lie subalgebras of rak{sl}_n, notably including the first to feature meanders with arbitrarily many parts, expanding the understanding of their structure.

Contribution

It extends known classifications by identifying a new broad family of Frobenius seaweed Lie algebras with complex meander structures.

Findings

Established a new family of Frobenius seaweed Lie algebras with arbitrarily many parts.

Expanded the classification of Frobenius seaweed Lie algebras.

Provided structural insights into the associated meanders.

Abstract

We extend the set of known infinite families of Frobenius seaweed Lie subalgebras of $\mathfrak{sl}_{n}$ to include a family which is the first non-trivial general family containing algebras whose associated meanders have an arbitrarily large number of parts.