It is genitive. Революция becomes революции in genitive, я changes to и. If it's been a long week already on Monday, I'm worried about you...
If you're uncertain, you can plug it in here: http://starling.rinet.ru/cgi-bin/morphque.cgi?flags=endnnnnp
i'm wondering if it's the partitive genitive thing... (хочу молока = i want (some) milk / не хочу молока = i don't want (any) milk).
if we think of revolution as more of an amorphous, uncountable thing rather than a specific event, that could work. but it would seem like a slightly different english translation actually would be in order:
мы не хотим революции (gen.) = we don't want (any) revolution.
мы не хотим революцию (acc.) = we don't want a/the revolution.
not sure that's really right, but it's my best guess for why the genitive ending here.
Yeah, that's about right. As I said before, using Genitive with negated verbs is a complicated issue in present day Russian. A century ago Genitive would be preferred. Nowadays is sounds very shabby and posh if you use it consistently regardless of context.
There is also that partitive thing: apperently, if you are talking about wanting a war or a revolution, the outcome is really uncertain and hard to predict, and the idea is abstract enough that, in fact, Genitive is often used even in positive sentences.
Which case is it exactly? I do not understand why the translation for the exercise is in plural if the english sentence is singular; "революции", or if it would be wrong to interpret this as accusative plural (which matches genitive singular according to the following website) https://cooljugator.com/run/%D1%80%D0%B5%D0%B2%D0%BE%D0%BB%D1%8E%D1%86%D0%B8%D1%8F.
Either the genitive or the accusative can be used as direct object of a negated verb. The rules for which is preferred in a given situation take up several pages in Wade's "Comprehensive Russian Grammar." Sometimes either is fine. Wade suggests using genitive in case of doubt. This is fine point of grammar that I really worry about. I still haven't recovered completely from perfective verbs.