Contact seaweeds II: type C

TL;DR

This paper extends the construction of contact forms from index-one seaweed subalgebras of special linear algebras to symplectic algebras using graph-theoretic and combinatorial methods.

Contribution

It generalizes previous results by including symplectic algebras, providing new contact form constructions for a broader class of seaweed subalgebras.

Findings

Contact forms constructed for index-one seaweed subalgebras of sp(2n)

Extension of previous linear algebra results to symplectic case

Graph-theoretic methods applied successfully to new algebra classes

Abstract

This paper is a continuation of earlier work on the construction of contact forms on seaweed algebras. In the prequel to this paper, we show that every index-one seaweed subalgebra of $A_{n-1}=\mathfrak{sl}(n)$ is contact by identifying contact forms that arise from Dougherty's framework. We extend this result to include index-one seaweed subalgebras of $C_{n}=\mathfrak{sp}(2n)$. Our methods are graph-theoretic and combinatorial.