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Results tagged with chevalley-groups
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user 12858
The Chevalley group is a way, uniform over all fields (and commutative rings), to define a split simple algebraic group of a given type.
3
votes
Accepted
Maximal split torus of universal chevalley group
By Lemma 28(b), $H$ is an abelian group generated by the $h_i(t)$'s (where $h_i = h_{\alpha_i}$), and since each $h_i$ is multiplicative (by Lemma 28(a)), the existence follows.
To prove uniqueness, …
- 6,614
1
vote
Twisted root subgroups in twisted Chevalley groups (reference request)
As indicated in Martin Seysen's comment, this construction can be found in Carter's book "Simple Groups of Lie type".
More precisely, this is Proposition 13.6.3, and your "naive approach" is indeed ex …
- 6,614