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  "body": "\n## Summary\n\nA Lie group action is a [[group action|0WCY42EV9V]] of a [[Lie group|7JBRGCVJRB]] on a [[smooth manifold|F45VQ47GPV]] such that the action map is smooth.\nIt is the precise form of continuous symmetry of a geometric space.\nOrbits of such actions are immersed submanifolds, and stabilisers are closed subgroups.\nDifferentiating the action turns elements of the Lie algebra into vector fields on the manifold.\n\n## Explanations\n\n### L1 human\n\nA Lie group action lets each element of a Lie group move the points of a smooth space.\nThe motion depends smoothly on both the element and the point.\nRotations of the plane about the origin are an example: rotating by $\\theta$ moves each point smoothly, and rotating twice adds the angles.\nThe orbits are the circles centred at the origin, together with the origin itself, which is fixed by every rotation.\n",
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