Please accept my apologies in advance for my simple question.


Let $W(2)$ be a simple Lie algebra over $\mathrm{GF}(2)$. We know that it has a basis with three elements like ${w\_1,w\_2,w\_3}$. I cannot understand how to compute the Lie bracket for this Lie algebra? $[w\_1,w\_2]=?$ $[w\_3,w\_1]=?$


I have already studied the paper from B. Eick.(<http://www.sciencedirect.com/science/article/pii/S0747717110000805>)



Understanding lie bracket of simple Lie algebra $W(2)$
The simple Lie algebra $W(1; \underline{2})^{(1)}$ over $GF(2)$ has a basis $\{w\_1,w\_2,w\_3 \}$ such that $[w\_i,w\_j]=w\_k$, where $\{i,j,k\}=\{1,2,3\}$. 


