A Lie group action is a smooth and continuous operation of a Lie group on a manifold, which allows for the exploration of the manifold's structure and its symmetries. This action can be thought of as a way for the elements of a Lie group to 'move' points in the manifold while preserving certain geometric properties. Understanding Lie group actions is crucial for analyzing orbits, stabilizers, and the classification of symmetric spaces, as they reveal how groups interact with geometrical objects.
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