A homogeneous polymerization catalyst system for polymerization or copolymerization of at least one alpha olefin has a Lewis acid, an alkyl aluminum in a hexane or a heptane, and at least one dry metallocene. The at least one dry metallocene has a transition metal compound. The Lewis acid is capable of forming an ion pair with the at least one dry metallocene. The homogeneous polymerization catalyst system produces a poly alpha olefin from alpha olefin monomers or mixed alpha olefins. A produced poly alpha olefin has a kinematic viscosity at 100 degrees Celsius ranging from 1 cSt to 1000 cSt.