English Dictionary

Lie group

noun

(topology) Any group that is a smooth manifold and whose group operations are differentiable.

A Lie group is a mathematical object that combines the concepts of a group and a differentiable manifold.

意味（1）

(topology) Any group that is a smooth manifold and whose group operations are differentiable.

Every connected Lie group is homotopically equivalent to its maximal compact subgroup. This reduces the study of the homotopy and homology of Lie groups to the compact case.