Examples
See Table of Lie groups for a list
- General linear group, special linear group
- SL2(R)
- SL2(C)
- Unitary group, special unitary group
- SU(2)
- SU(3)
- Orthogonal group, special orthogonal group
- Rotation group SO(3)
- SO(8)
- Generalized orthogonal group, generalized special orthogonal group
- The special unitary group SU(1,1) is the unit sphere in the ring of coquaternions. It is the group of hyperbolic motions of the Poincaré disk model of the Hyperbolic plane.
- Lorentz group
- Spinor group
- Symplectic group
- Exceptional groups
- G2
- F4
- E6
- E7
- E8
- Affine group
- Euclidean group
- Poincaré group
- Heisenberg group
Read more about this topic: List Of Lie Groups Topics
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“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
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—Bernard Mandeville (1670–1733)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)