Unfortunately (IMO), key mapping in ST:S is tied to the CTL key, which kind of invalidates the usefulness of keyboard mapping Maybe this should be reviewed?
So far, this is what I've found:

CTL+RET : end turn
CTL+HOME : center on the center of the galaxy
CTL+END : center on homeworld
CTL+LMBdrag : drag map
CTL+[+] : zoom in
CTL+[-] : zoom out

BTW, the +/- keys in the keypad do not work (for zooming), not sure it's intended or not.
Also, I'm used to have the HOME key center on the homeworld, but maybe that's just me?
I understand the use of the CTL key with RET though, to prevent accidents.

I read somewhere someone asking for a way to end turn from any screen. F1 CTL+RET

Oh, those were not intended? Ooops. Anyways, I guess it's good to know they work..
Maybe you could use F7~F12 to implement additional screens like System Overview, Empire Overview, Fleet Overview, etc.

Oh, and BTW, maybe a testing ("cheat") key for removing/toggling fog of war wouldn't hurt? (Ins/Del?) Maybe even making it an option in the Options screen?

If the home/end keys move the focus to the map corners, then perhaps the 5 key on the number pad could be used to take you to your homeworld? That or make it Ctrl+H...or both.

Page up and page down should take you to the opposite map corners if they don't already. I still haven't got my computer back so can't test whether they do. I've temporarily borrowed my sister's laptop though to type this hehe.