Contact Seaweeds

TL;DR

This paper investigates contact structures on certain Lie algebras, proving that index-one type-A seaweed algebras are necessarily contact and providing explicit examples and construction methods.

Contribution

It establishes a new connection between index-one type-A seaweed algebras and contact structures, including explicit construction techniques.

Findings

Index-one type-A seaweed algebras are contact.

Explicit examples of contact seaweed algebras are provided.

A method for constructing contact seaweed algebras is introduced.

Abstract

A ($2k+1$)$-$dimensional contact Lie algebra is one which admits a one-form $\varphi$ such that $\varphi \wedge (d\varphi)^k\ne0$. Such algebras have index one, but this is not generally a sufficient condition. Here we show that index-one type-A seaweed algebras are necessarily contact. Examples, together with a method for their explicit construction, are provided.