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The Chevalley group is a way, uniform over all fields (and commutative rings), to define a split simple algebraic group of a given type.
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Universal Chevalley group associated to $D_l$
Consider the simple Lie algebra $D_l$. Consider the universal Chevalley group $G$ over a field $K$ associated to it. Then $G$ is a subgroup of the orthogonal group $O_{2l}(K, f)$ where $f$ is the qua …