Exceptional Object - Simple Lie Groups

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, CO, HO and OO 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:

    Even the simple act that we call “going to visit a person of our acquaintance” is in part an intellectual act. We fill the physical appearance of the person we see with all the notions we have about him, and in the totality of our impressions about him, these notions play the most important role.
    Marcel Proust (1871–1922)

    A state that denies its citizens their basic rights becomes a danger to its neighbors as well: internal arbitrary rule will be reflected in arbitrary external relations. The suppression of public opinion, the abolition of public competition for power and its public exercise opens the way for the state power to arm itself in any way it sees fit.... A state that does not hesitate to lie to its own people will not hesitate to lie to other states.
    Václav Havel (b. 1936)

    If we can learn ... to look at the ways in which various groups appropriate and use the mass-produced art of our culture ... we may well begin to understand that although the ideological power of contemporary cultural forms is enormous, indeed sometimes even frightening, that power is not yet all-pervasive, totally vigilant, or complete.
    Janice A. Radway (b. 1949)