Notation on Lie groups
In this package,the notation introduced in Manifolds.jl Notation is used with the following additional parts.
| Symbol | Description | Also used | Comment |
|---|---|---|---|
| $∘$ | a group operation | ||
| $c_g:\mathcal G → \mathcal G$ | the conjugation map (with g) | ||
| $\mathrm{e}$ | identity element of a group | ||
| $g, h, k$ | elements on a (Lie) group. Sometimes called points. | $g_1, g_2, ...$ | |
| $\mathfrak g$ | a Lie algebra | ||
| $\mathcal{G}$ | a (Lie) group | ||
| $λ_g: \mathcal G → \mathcal G$ | the left group operation map $λ_g(h) = g∘h$ | ||
| $ρ_g: \mathcal G → \mathcal G$ | the right group operation map $ρ_g(h) = h∘g$ | ||
| $σ: \mathcal G × \mathcal M$ | a left group action | $σ_g(p)$ to emphasize a fixed group element | |
| $τ: \mathcal M × \mathcal G$ | a right group action | $σ_\mathrm{R}$ | $τ_g(p)$ to emphasize a fixed group element |