definition of Lie group
Topics
About: group
About: \(C^\infty\) manifold
The table of contents of this article
Starting Context
- The reader knows a definition of group.
- The reader knows a definition of \(C^\infty\) manifold.
- The reader knows a definition of finite-product \(C^\infty\) manifold with boundary.
Target Context
- The reader will have a definition of Lie group.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\(*G\): \(\in \{\text{ the groups }\} \cap \{\text{ the } C^\infty \text{ manifolds } \}\)
//
Conditions:
\(m: G \times G \to G, (g_1, g_2) \mapsto g_1 g_2 \in \{\text{ the } C^\infty \text{ maps }\}\), called "multiplication map"
\(i: G \to G, g \mapsto g^{-1} \in \{\text{ the } C^\infty \text{ maps }\}\), called "inversion map"
//
