= Chevalley basis
{c}
A Chevalley basis of a complex <semisimple Lie algebra> consists of suitable coroot elements and one vector $e_\alpha$ in each <root space>, chosen so all <Lie bracket> structure constants are integers. In particular $[e_\alpha,e_\beta]=N_{\alpha,\beta}e_{\alpha+\beta}$ when the sum is a <root>, with $N_{\alpha,\beta}=\pm(p+1)$ where $\beta-p\alpha$ is the last negative-direction root in the <root string>. For independent roots with no root sum the bracket is zero. The integral lattice makes reduction to other fields possible.
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