Abstract: A catalyst for addition polymerization obtained by bringing the following (A) into contact with (B) a specific organic aluminum compound and/or aluminoxane, and (C) a specific boron compound, and a process for producing an addition polymer with the same. (A) a transition metal compound represented by the formula (3): wherein M represents a titanium atom, zirconium atom or hafnium atom in the +3 oxidation state; Cp1 represents a group having a cyclopentadiene type anion skeleton; J represents an atom of XIV group in the Periodic Table of the Elements; each of R2 and R3 independently represents a hydrogen atom, halogen atom, alkyl group, aralkyl group, aryl group, substituted silyl group, alkoxy group, aralkyloxy group, aryloxy group or di-substituted amino group; m represents an integer of from 0 to 4; E represents an oxygen atom or sulfur atom; R1 represents an alkyl group, aralkyl group, aryl group or substituted silyl group; each of two Xs independently represents a hydrogen atom, halogen atom, alkyl group, aralkyl group, aryl group, substituted silyl group, alkoxy group, aralkyloxy group, aryloxy group or di-substituted amino group; D represents a neutral ligand coordinated on M; and n represents an integer of from 0 to 2.
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