On toral posets and contact Lie algebras

TL;DR

This paper introduces a combinatorial method for generating contact Lie poset algebras of arbitrary chain length, aiming to fully characterize such algebras within type-A Lie poset structures.

Contribution

It extends previous work by providing a new combinatorial procedure for constructing contact Lie poset algebras with chains of any size, and conjectures this method is comprehensive.

Findings

Developed a combinatorial procedure for contact Lie poset algebras

Applied the method to generate algebras with arbitrary chain lengths

Conjecture that the construction provides a complete characterization

Abstract

A $(2k+1)-$dimensional Lie algebra is called contact if it admits a one-form $\varphi$ such that $\varphi\wedge(d\varphi)^k\neq 0.$ Here, we extend recent work to describe a combinatorial procedure for generating contact, type-A Lie poset algebras whose associated posets have chains of arbitrary cardinality, and we conjecture that our construction leads to a complete characterization.