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One parameter subgroup

Ciro Santilli (@cirosantilli, 37) ... Geometry Differential geometry Lie group Important Lie group Matrix Lie group Lie algebra of a matrix Lie group
Updated 2025-07-16  0 By others on same topic  0 Discussions Create my own 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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