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One parameter subgroup

The one parameter subgroup of a Lie group for a given element

M

of its Lie algebra is a subgroup of

G

given by:

e^{t M} \in G ∣ t \in R

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

S O (3)

, the rotation group.

One parameter subgroups can be seen as the continuous analogue to the cycle of an element of a group.

 Ancestors

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