Hey Joe,

>
> I guess I am inclined to try to build this thing and see who is interested 
> in it. The ticket you linked is very helpful to me. 
>

Let me know what you need from me wrt #14901 or any additional feature 
requests.

>
> I'm interested to know more about your plans for Lie groups and Groups of 
> Lie type. 
>

   Right now, I don't have any immediate plans as I have many other things 
to do at present (one of which is getting back to polishing #14901). I 
would like to have Lie groups (over CC) use the SageManifolds framework 
rather than being abstract parents, and introduce their representation 
theory. However, I would be happy to review and offer my thoughts.

>
> In some sense it seems to me that the objects I'm really working with are 
> Group schemes defined using a certain presentation. If I have a group 
> scheme I can take real points to get a lie group or points over a finite 
> field to get a finite group of Lie type. On the other hand depending on 
> what one wants to do with the Lie group/FGLT, this might have little to 
> nothing to do with how one wants to think about them.
>

   That is probably the best way to think about how to implement things: 
what do you want to be able to do with them or learn from the 
implementation (at least, this is one of the ways I learn new math things). 
>From there, that can tell you what features and functionality you want, 
which will influence your design decisions.

Best,
Travis

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