- Chi : G -> R^n. This is the coordinate function on the group manifold.
- Chi^-1 : R^n -> G. The inverse of Chi.
- e \in G. The identity element.
- inverse: G -> G. The inverse function (on the group manifold: g -> g^-1).
- *: GxG -> G. The group multiplication function.

`<chart>`object. Note carefully the signatures of these functions; in particular, note that only Chi and Chi^-1 deal with R^n while all others deal directly with group elements.

See lie-group-SO3.ss for an example of how this is done. It's a bit
tricky, because the `<chart>` (which contains Chi and Chi^-1) must take
and produce objects of the `<lie-group-element>` class, which require
the `<lie-group>` class for one of the slots; but the `<lie-group>` class
requires the `<chart>` object, so they must be recursively defined.

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