Simple Lie Groups
The simple Lie groups form a number of series (classical Lie groups) labelled A, B, C and D. In addition we have the exceptional groups G2 (the automorphism group of the octonions), F4, E6, E7, E8. These last four groups can be viewed as the symmetry groups of projective planes over O, C⊗O, H⊗O and O⊗O respectively, where O is the octonions and the tensor products are over the reals.
The classification of Lie groups corresponds to the classification of root systems and so the exceptional Lie groups correspond to exceptional root systems and exceptional Dynkin diagrams.
Read more about this topic: Exceptional Object
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