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| | What IS a Lie Group? |
 | | The Bn and Dn are real rotations, denoted Spin(2n+1) and Spin(2n), and are called Spin groups, the double covers of special Orthogonal groups; the An are complex generalized rotations, denoted SU(n+1), and are called special Unitary groups; and the Cn are quaternionic generalized rotations, denoted Sp(n), and are called Symplectic groups. |
 | | F4 is the automorphism group of 3x3 matrices of octonions o11 o12 o13 o21 o22 o23 o31 o32 o33 such that o11, o22, and o33 are real (have no imaginary part), and o12, o13, o23 are the octonion conjugates of o21, o31, o32 respectively. |
 | | A Lie algebra is a logarithm of a Lie group, and a Lie group is an exponential of a Lie algebra. |
| akbar.marlboro.edu /~mahoney/groups/Lie.html (2525 words) |
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