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In mathematics, a Lie group, named after Norwegian mathematician Sophus Lie (IPA pronunciation: , sounds like "Lee"), is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. Lie groups represent the best developed theory of continuous symmetry of mathematical objects and structures. This makes Lie groups tools for nearly all parts of contemporary mathematics, as well as for modern theoretical physics, especially particle physics.