Yes you can buy fractions, but a VIVA Crown will only be really useful when you have a whole crown. Then you can 'register' a crown, so it gets officially and you can use it. If you now have one crown and you have a business (in real life, that is not minting VIVA), you are permitted to mint VIVA with the Treasury Rights.

I can't tell you how exactely it works, for that you maybe need to read the whitepaper.