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In the screen showing structures of a province, you have the option to build a manufactory (click on the northwest corner). You can then select from the manufactories available. A Fine Arts Academy, like all manufactories, costs a lot of money to build, but gives you a small amount of income per year and allows you to recover stability more quickly.
 
Actually they give you a small income per month, 6 if built anywhere but your capital and 12 if built in your capital. So a finearts academy in your capital means +5 every month on your stability 'research' and 1 extra ducat every month for the rest of the game... Pretty cool ... :) But as all cool stuff, mightely expensive :)

Cobos
 
Actually, you could hope for a random event like I had, where my naval manufactory caught fire and burned to the ground -- then I could rebuild anything in its place. :)