The breadth of Lie poset algebras

Abstract

The breadth of a Lie algebra L is defined to be the maximal dimension of the image of $a{d}_x=[x,-]:L\to L$, 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.

COMMUNICATED BY:

• M. Chebotar

Keywords:

• Breadth
• Lie algebra
• poset

2020 Mathematics Subject Classifications:

• 17B30
• 05E16

Disclosure statement

No potential conflict of interest was reported by the author(s).