Kubota tractor 12 volt charging system?

ok it's been a while since I had a meter in my hand so forgive me...Got this kubota tractor that is not charging...battery goes dead after running for several hours next day dead battery....so battery looks good (don't have a load tester) Ive got 30is volts ac comming out of the alt (or whatever they call that) and I ve got between 7 and 13 volts dc comming out of inverter depending upon rpm so what else is there? Cant I tap into the wires comming out of inv and hook to battery? Charging through the negative terminal? Can ya help me?