How can I find a Chevalley basis of a type $B_2$ when the related Lie algebra is defined as a linear Lie algebra of elements of the form $$x= \begin{pmatrix} 0 & b_1 & b_2 \\ c_1 & m & n \\ c_2 & p & q \end{pmatrix},$$ where $c_1=-b_2^t$, $c_2=-b_1^t$, $q=-m^t$, $n^t=-n$, $p^t=-p$?
When trying to find such a base, the constraints, especially $[x_{\alpha}x_{\beta}]=c_{\alpha,\beta}x_{\alpha+\beta}$ for $\alpha,\beta$ independent, and $\alpha+\beta$ being a root, turn out to be very hard to follow.
Thank you~ :)