朴素李理论

1  Geometry of complex numbers and quaternions
　1.1  Rotations of the plane
　1.2  Matrix representation of complex numbers
　1.3  Quaternions
　1.4  Consequences of multiplicative absolute value
　1.5  Quaternion representation of space rotations
　1.6  Discussion
2  Groups
　2.1  Crash course on groups
　2.2  Crash course on homomorphisms
　2.3  The groups SU(2) and SO(3)
　2.4  Isometries of * and reflections
　2.5  Rotations of R4 and pairs of quaternions
　2.6  Direct products of groups
　2.7  The map from SU(2)xSU(2) to SO(4)
　2.8  Discussion
3 Generalized rotation groups
　3.1  Rotations as orthogonal transformations
　3.2  The orthogonal and special orthogonal groups
　3.3  The unitary groups
　3.4  The symplectic groups
　3.5  Maximal toil and centers
　3.6  Maximal toil in SO(n), U(n), SU(n), Sp(n)
　3.7  Centers of SO(n), U(n), SU(n), Sp(n)
　3.8  Connectedness and discreteness
　3.9  Discussion
　……