The steel container is coated with carbon (graphite) and this is the negative electrode (cathode).

Electrolysis of the alumina/cryolite solution gives aluminium at the cathode and oxygen at the anode.

Al³⁺  +  3e^-       Al (aluminium metal at the (-)cathode)
2O^2-  -  4e^-       O₂ (oxygen gas at the (+)anode)

Aluminium is more dense than the alumina/cryolite solution, and so falls to the bottom of the cell where it can be tapped off as pure liquid metal.

The overall reaction is

aluminium oxide       aluminium + oxygen
2Al₂³⁺O₃^2-_(l)                 4Al_(l)   +     3O_2(g)

Oxygen is discharged at the positive carbon (graphite) anode.Oxygen reacts with the carbon anode to form carbon dioxide gas.

carbon + oxygen    carbon dioxide
C_(s)  +    O_2(g)             CO_2(g)

The carbon anode slowly reacts to make carbon dioxide and needs to be replaced regularly.