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).

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