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
Famous quotes containing the words simple, lie and/or groups:
“There was a deserted log camp here, apparently used the previous winter, with its hovel or barn for cattle.... It was a simple and strong fort erected against the cold, and suggested what valiant trencher work had been done there.”
—Henry David Thoreau (18171862)
“My brother Toby, quoth she, is going to be married to Mrs. Wadman. Then he will never, quoth my father, be able to lie diagonally in his bed again as long as he lives.”
—Laurence Sterne (17131768)
“Belonging to a group can provide the child with a variety of resources that an individual friendship often cannota sense of collective participation, experience with organizational roles, and group support in the enterprise of growing up. Groups also pose for the child some of the most acute problems of social lifeof inclusion and exclusion, conformity and independence.”
—Zick Rubin (20th century)