The breadth of Lie poset algebras

TL;DR

This paper explores the concept of breadth in Lie algebras defined by posets, providing combinatorial formulas for three specific families and initiating a systematic study of this property.

Contribution

It introduces the notion of breadth for Lie poset algebras and derives explicit combinatorial formulas for three families, advancing understanding of their structure.

Findings

Derived combinatorial formulas for the breadth of three Lie poset algebra families

Initiated systematic study of breadth in Lie poset algebras

Connected algebraic properties with combinatorial structures

Abstract

The breadth of a Lie algebra $L$ is defined to be the maximal dimension of the image of $ad_x=[x,-]:L\to L$, for $x\in L$. Here, we initiate an investigation into the breadth of three families of Lie algebras defined by posets and provide combinatorial breadth formulas for members of each family.