| 释义 |
Lie group A Lie group G is a group G that also has the structure of a smooth manifold. Further, the group operations of multiplication G×G → G and inversion G → G must be smooth. An example is S1 considered as unit modulus complex numbers under multiplication. Real and complex matrix groups are further examples. The Lie correspondence connects Lie groups and Lie algebras, and there is a rich representation theory of compact Lie groups largely due to Weyl. See also topological group.
|