[yeung]

In heating styrene to make polystyrene,kerosene is used as a catalyst.But is there chemical reactions taking place?

[ATMyller]

The chemical reaction making polystyrene, as well as most polyolefins, is free radical reaction called addition polymerization. Addition polymeriztion is usually initiated by heating a radical producing compound etc. a peroxide.
I've never heard that kerosene would be used as a catalyst, it's more like a solvent for the reaction since free radical addition polymerization doesn't require catalyst once it has been initiated.