Derivations of Lie Algebras of Dominant Upper Triangular Ladder Matrices

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 $char(F) \neq 2, 3$.