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  "body": "\n## Summary\n\nA Chevalley group is a group of automorphisms of a simple Lie algebra rebuilt over an arbitrary field.\nThe rebuilding uses the integral structure given by a Chevalley basis.\nClaude Chevalley introduced this construction in 1955.\nIt gives, in a uniform way, a simple group for each simple complex Lie algebra and each field, apart from a few small exceptions.\nOver finite fields these groups give most of the families of finite simple groups of Lie type, including new families of exceptional type.\n\n## Explanations\n\n### L1 human\n\nA complex simple Lie algebra, such as the algebra of $2 \\times 2$ matrices of trace $0$, has a basis in which all the structure constants are integers.\nBecause of this, one can reduce it modulo a prime, or more generally build a copy of it over any field.\nThe Chevalley group is generated by exponentials of certain nilpotent operators on this copy.\nFor the algebra of type $A_1$ and a field $K$, the result is the group $\\mathrm{PSL}_2(K)$.\n",
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