Process for producing a polymer of an α-olefin and lubricant

A process for producing a polymer comprising one or more α-olefins, said process comprising

• polymerizing one or more α-olefins having at least 4 carbon atoms in the presence of a catalyst, said catalyst comprising:
• (A) at least one compound represented by formula (I):
• wherein
• R1 to R6 and X1 to X2 each independently represent a hydrogen atom, a halogen atom, a hydrocarbon group having 1 to 20 carbon atoms, a hydrocarbon group having 1 to 20 carbon atoms and a halogen atom, a group having silicon, a group having oxygen, a group having sulfur, a group having nitrogen or a group having phosphorus;
• adjacent groups among groups represented by R1 to R6 and X1 to X2 may form a ring by forming bonds between each other;
• Y1 to Y2 each independently represent a divalent group which forms a bond between two ligands and is selected from the group consisting of hydrocarbon groups having 1 to 20 carbon atoms, hydrocarbon groups having 1 to 20 carbon atoms and a halogen atom, a group having silicon, a group having germanium, a group having tin, —O—, —CO—, —S—, —SO2—, —NR13—, —PR13—, —P(O)R13—, —BR13— and —AlR13—;
• R13 representing a hydrogen atom, a halogen atom, a hydrocarbon group having 1 to 20 carbon atoms or a hydrocarbon group having 1 to 20 carbon atoms and a halogen atom, and
• M1 represents a transition metal of Groups 4 to 6 of the Periodic Table;
• and
• (B) at least one compound selected from (b-1) organoaluminum oxy compounds and (b-2) ionic compounds which can be converted into cations by reaction with the transition metal compounds of component (A), and
• hydrogenating the polymer.