Example
Unit Circle
The unit circle in $\mathbb{C}$ denoted $$S^1 = \{e^{i\theta} \colon \theta \in [0,2\pi)\} = \{z \in \mathbb{C}\colon |z|= 1\}$$ endowed with group multiplication as
\[
e^{i\alpha} \cdot e^{i\beta} = e^{i(\alpha+\beta)}
\]
is a Lie group (Definition Lie Group).
Depends on
Used in
Dependency Graph
flowchart LR
classDef current fill:#6366f1,color:#fff,stroke:#4f46e5
ne5f4203c["Lie Group"]
n383b5512["Unit Circle"]:::current
n8aabc776["Proposition"]
ne5f4203c --> n383b5512
n383b5512 --> n8aabc776
click ne5f4203c "../objects/e5f4203c.html" "_self"
click n8aabc776 "../objects/8aabc776.html" "_self"