= 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:
$$
{ e^{tM} \in G | t \in \R }
$$
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 SO(3)>, the <rotation group>.
One parameter subgroups can be seen as the continuous analogue to the <cycle of an element of a group>.
Back to article page