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by Ciro Santilli (@cirosantilli, 37)

One parameter subgroup

 ... Geometry Differential geometry Lie group Important Lie group Matrix Lie group Lie algebra of a matrix Lie group
 0 By others on same topic  0 Discussions  Updated 2025-05-29  +Created 1970-01-01  See my version
The one parameter subgroup of a Lie group for a given element M of its Lie algebra is a subgroup of G given by:
etM∈G∣t∈R
(1)
Intuitively, M is a direction, and t is how far we move along a given direction. This intuition is especially vivid in for example in the case of the Lie algebra of SO(3), the rotation group.
One parameter subgroups can be seen as the continuous analogue to the cycle of an element of a group.

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  • Cycle of an element of a group
  • Lie algebra of a matrix Lie group

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