Extend `identity_element` to more manifolds

[mateuszbaran]

See https://github.com/JuliaRobotics/IncrementalInference.jl/issues/1527 for discussion.

[kellertuer]

Isn't this already resolved now with #503 ?

[mateuszbaran]

No, these two things are unrelated.

[kellertuer]

AH, ok, then I mixed that up.

[kellertuer]

But still, to be precise I would only like to add identity_element to Lie groups to be precise?

[mateuszbaran]

I think the idea would be to also define identity_element to manifolds that can have a group structure but I'm not sure it's a good idea anyway.

[kellertuer]

I see that point, but I would prefer to be a little more precise. For example if the have GL(n) which has as manifold Euclidean(n,n) (not all of that, ok, I am not creative enough just now for a better example) what is the right identity? For GL(n) it would ne matrix multiplication so I but for the translation group on Euclidean(n,n) its zeros(n,n). So just the manifold might not be enough to know the group structure and hence the identity element?

[mateuszbaran]

I don't think we currently have multiple groups structures with different identity elements (Euclidean and GL are topologically different) but in the future we could encounter such case, right.

[kellertuer]

Yes (that's why I was lazy with an example).