= Adjoint Chevalley group
Fix a <Chevalley basis> and its integral lattice. The adjoint Chevalley group over a <field> is generated by the root operators obtained from the integral divided-power polynomials $x_\alpha(t)=\sum_j t^j(\operatorname{ad}e_\alpha)^j/j!$ on that lattice. The coefficients are first computed over the integers and then reduced to the field; factorials need not be invertible there. This is the adjoint construction; other weight lattices give other isogeny forms of <groups> of Lie type.
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