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:

    Poetry is the most direct and simple means of expressing oneself in words: the most primitive nations have poetry, but only quite well developed civilizations can produce good prose. So don’t think of poetry as a perverse and unnatural way of distorting ordinary prose statements: prose is a much less natural way of speaking than poetry is. If you listen to small children, and to the amount of chanting and singsong in their speech, you’ll see what I mean.
    Northrop Frye (1912–1991)

    A box of teak, a box of sandalwood,
    A brass-ringed spyglass in a case,
    A coin, leaf-thin with many polishings,
    Last kingdom of a gold forgotten face,
    These lie about the room....
    Philip Larkin (1922–1986)

    Some of the greatest and most lasting effects of genuine oratory have gone forth from secluded lecture desks into the hearts of quiet groups of students.
    Woodrow Wilson (1856–1924)