Contact seaweeds

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

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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

Authors

Vincent E. Coll Jr.
Lehigh University Bethlehem, PA United States

Nicholas Mayers
Lehigh University Bethlehem, PA United States

Nicholas Russoniello
Lehigh University Bethlehem, PA United States

Gil Salgado
Universidad Autónoma de San Luis Potosí San Luis Potosí Mexico

Vol. 320, No. 1, 2022

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

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors