Exceptional Cases
For the so-called exceptional cases see G2, F4, E6, E7, and E8. These cases are deemed 'exceptional' because they do not fall into infinite series of groups of increasing dimension. From the point of view of each group taken separately, there is nothing so unusual about them. These exceptional groups were discovered around 1890 in the classification of the simple Lie algebras, over the complex numbers (Wilhelm Killing, re-done by Élie Cartan). For some time it was a research issue to find concrete ways in which they arise, for example as a symmetry group of a differential system.
See also E7½
Read more about this topic: Simple Lie Group
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