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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~ :)

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