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Results tagged with exceptional-groups
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user 110362
Exceptional Lie groups G2, F4, E6, E7, E8 of dimensions 14, 52, 78, 133, 248 were obtained as result of classification of simple Lie groups performed by Killing and Elie Cartan. The tool used in classification is Dynkin diagram and root system of vectors in Lie algebra of the group. The remaining Lie groups form four infinite families of transformations of n-dimensional space over real (odd and even), complex and quaternionic field.
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Does $G_2(\mathbb{Z})$ depend on the choice of an integral model?
The short answer is no, because a Chevalley group has infinitely many $\mathbb{Z}$-points (even Zariski dense by the Borel density theorem).
For the long answer, let me first completely describe all $ …
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