Contact seaweeds

Vincent E. Coll Jr., Nicholas Mayers, Nicholas Russoniello and Gil Salgado

Vol. 320 (2022), No. 1, 45–60

DOI: 10.2140/pjm.2022.320.45

Abstract

A ($2k+1$)-dimensional contact Lie algebra is one which admits a one-form $\phi$ such that $\phi \wedge {(d\phi )}^k\ne 0$. 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.

Keywords

contact Lie algebra, contact structure, Frobenius Lie algebra, seaweeds, meanders, regular one-forms

Mathematical Subject Classification

Primary: 17Bxx

Secondary: 53D10

Milestones

Received: 14 January 2021

Revised: 8 June 2022

Accepted: 16 July 2022

Published: 16 October 2022