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  "body": "\n## Summary\n\nA one-parameter subgroup of a topological group $G$ is a continuous [[group homomorphism|0JYTG5K9Y4]] from the additive group $\\R$ into $G$.\nIn a [[Lie group|7JBRGCVJRB]], it is a smooth curve through the identity along which the group law becomes addition of the parameter.\nOne-parameter subgroups of a Lie group correspond to the tangent vectors at the identity, which is how the exponential map is built.\n\n## Explanations\n\n### L1 human\n\nA one-parameter subgroup is a way to move steadily through a group.\nMoving for time $s$ and then for time $t$ is the same as moving for time $s + t$.\nTurning a wheel at constant speed is a picture: the rotation after time $t$ is a rotation by the angle $ct$.\nIn the group of invertible matrices, $t \\mapsto e^{tA}$ is a one-parameter subgroup for each square matrix $A$.\nFor $A = \\begin{pmatrix} 0 \u0026 -1 \\\\ 1 \u0026 0 \\end{pmatrix}$, it gives the rotations by angle $t$ of the plane.\n",
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