Pure aluminium oxide is not used for electrolysis. Its melting point is too high, and it is not a good conductor. Instead it is dissolved at about 5% concentration in molten sodium aluminium fluoride ("cryolite").
The chemistry used to obtain pure aluminium oxide ("alumina") from bauxite was first developed by the German chemist Karl Bayer in 1888, and the process is still referred to as the "Bayer Process".
Bayer Process Chemistry
Aluminium forms an amphoteric oxide that will react with sodium hydroxide,
whereas the other metal oxides in bauxite do not.
During electrolysis the aluminium oxide is dissolved
in "cryolite", which is sodium aluminium fluoride (Na3AlF6).
Cryolite is made using sodium aluminate and hydrogen fluoride, which
is manufactured from the mineral fluorspar using sulphuric acid.