"I support the division..." and "I support dividing..." both indicate support for the act of dividing, whether you have the authority of decide on whether or not the division is happening.

If I'm at a birthday party and there's one piece of cake left but three people still hungry, I could say "I support the division of the piece of cake" or "I support dividing the piece of cake" even if the person celebrating the birthday is the ultimate authority on whether we will divide the cake. I'd convey the same idea, just with slightly different words, and likely different intonation, too.