I read the exercise 4.4 in the book Introduction to Lie algebras and representation theory of J. Humphreys, and I do not quite understand the sentence :
We start with $L\leq\mathfrak{gl}(p,F)$ as in Exercise 4.3, and let $M:=L+F^p$, the direct sum. We then make $M$ into a Lie algebra by decreeing that $F^p$ is abelian, while $L$ has its usual product and acts on $F^p$ in the given way.
Could some one tell me what the Lie bracket inside $M$ is? Many thanks in advance.