Lie group implementation

[Jia En Toh]

Hi

On the ideas page it was noted that it was possible to extend the group module to include lie groups. The sympy.diffgeom module exists and has many features but it doesn't have lie groups. On the other hand there is already a lie algebra module that any lie group class would have to interact with since the tangent space at the identity is the lie algebra of that group. 

Matrix lie groups are easier to work with and require less differential geometry to define, so perhaps they wouldn't need to be integrated so heavily with diffgeom. 

What would be most useful? Would it be feasible to define a general lie group with multiplication operations? 

I notice that lie groups have been discussed many times over the years, and it seems that there are some technical difficulties. 

If I restricted myself to SO(n), SU(n), GL(n), Sp(n) (or just one or two of them) would this be more manageable? These all also happen to be reductive which is more interesting for many mathematicians anyway. 

Regards

Jia En