Compact Group - Compact Lie Groups

Compact Lie Groups

Lie groups form a very nice class of topological groups, and the compact Lie groups have a particularly well-developed theory. Basic examples of compact Lie groups include

  • the circle group T and the torus groups Tn,
  • the orthogonal groups O(n), the special orthogonal group SO(n) and its covering spin group Spin(n),
  • the unitary group U(n) and the special unitary group SU(n),
  • the symplectic group Sp(n),
  • the compact forms of the exceptional Lie groups: G2, F4, E6, E7, and E8,

The classification theorem of compact Lie groups states that up to finite extensions and finite covers this exhausts the list of examples (which already includes some redundancies).

Read more about this topic:  Compact Group

Famous quotes containing the words compact, lie and/or groups:

    “The Puritans, to keep the remembrance of their unity one with another, and of their peaceful compact with the Indians, named their forest settlement CONCORD.”
    —Ralph Waldo Emerson (1803–1882)

    “America is, therefore the land of the future, where, in the ages that lie before us, the burden of the World’s history shall reveal itself. It is a land of desire for all those who are weary of the historical lumber-room of Old Europe.”
    —Georg Wilhelm Friedrich Hegel (1770–1831)

    “Only the groups which exclude us have magic.”
    —Mason Cooley (b. 1927)