Process for producing alpha-olefin polymer

Claim 1

A catalyst for polymerization of olefins, comprising a) a metallocene compound, b) an ionizing ionic compound, c) organoaluminum compound, and d) a Lewis base compound: a) the metallocene compound being represented by General Formula (1) or (2): where Cp¹, Cp², Cp³ and Cp⁴ are independently a substituted or unsubstituted cyclopentadienyl, indenyl, or fluorenyl group; R¹ is a substituted or unsubstituted alkylene, dialkylsilanediyl, dialkylgermanediyl, alkylphosphinediyl, or alkylimino group, and R¹ links Cp¹ with Cp² by bridging; M is a titanium atom, a zirconium atom, or a hafnium atom; and R², R³, R⁴ and R⁵ are independently a hydrogen atom, a halogen atom, a hydroacrbon group of 1 to 12 carbon atoms, an alkoxy group, or an aryloxy group; b) the ionizing ionic compound being a compound which is capable of changing the above a) metallocene compound into a cationic metallocene compound and does not react further with the formed cationic metallocene compound; c) the organoaluminum compound being represented by General Formula (3): where R⁶, R 6' , and R 6'' are independently a hydrogen atom, a halogen atom, an amino group, an alkyl group, an alkoxy group, or an aryl group, and at least one of R⁶, R 6' , and R 6'' is an alkyl group; d) the Lewis base compound being capable of donating an electron to the formed cationic metallocene compound.