Derivations of Lie Algebras of Dominant Upper Triangular Ladder Matrices

TL;DR

This paper explicitly describes the structure of Lie algebras formed by ladder matrices associated with dominant upper triangular ladders and characterizes their derivations over fields with specific characteristics.

Contribution

It provides a complete characterization of derivations for Lie algebras of ladder matrices and their commutators, extending understanding of their algebraic structure.

Findings

Derived explicit descriptions of Lie algebras of ladder matrices.

Characterized derivations over fields with char(F) ≠ 2 and 3.

Extended results to strongly dominant upper triangular ladders.

Abstract

We explicitly describe the Lie algebras $M_L$ of ladder matrices in $M_n$ associate with dominant upper triangular ladders $L$, and completely characterize the derivations of these $M_L$ over a field $F$ with $char(F) \neq 2$. We also completely characterize the derivations of Lie algebras $[M_L, M_L]$ where $L$ are strongly dominant upper triangular ladders and $char(F) \neq 2, 3$.