The role of fluorspar (CaF2) which is added in small quantities in the electrolytic reduction of alumina dissolved in fused cryolite (Na3AlF6) is:
to make the fused mixture very conducting
The conductivity of the electrolyte which is a mixture of Alumina, cryolite and fluorospar increases by addition of a small amount of (CaF2) due to its high ionic nature.