grupo de Lie
1. A mathematical group that is also a smooth manifold, where the group operations (multiplication and inversion) are smooth functions. Named after the Norwegian mathematician Sophus Lie.
The group of rotations in three-dimensional space forms a Lie group.
O grupo de rotações no espaço tridimensional forma um grupo de Lie.
2. In abstract algebra and differential geometry, a structure combining algebraic and topological properties that allows the study of continuous symmetries.
Lie groups are fundamental in theoretical physics and represent continuous symmetry transformations.
Grupos de Lie são fundamentais na física teórica e representam transformações de simetria contínua.
This is a technical mathematical term with no cultural significance beyond academic use. The term is named after Sophus Lie, a 19th-century Norwegian mathematician, and is used uniformly across English-speaking and Portuguese-speaking academic communities. It is primarily encountered in advanced mathematics, theoretical physics, and engineering curricula.
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