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Results tagged with lie-groups
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user 12858
Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.
4
votes
Ree groups and Moufang octagons
Only having $k$ as subfield of $\ell$ is not sufficient (for both questions). The Ree groups (and the generalized octagons) are determined by a pair $(k, \theta)$, where $k$ is a field of characterist …
- 6,614
13
votes
Accepted
Constructing $E_8$ from its branching to $A_8$
An excellent reference for this kind of descriptions (and for many other facts about $E_8$!) is Skip Garibaldi's paper "$E_8$, the most exceptional algebraic group" in the Bulletin of the AMS (here).
…
- 32.5k
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