The fact that BCJ numerators can be tuned to have antisymmetry and satisfy Jacobi identity leads to the speculation of a underlying Lie algebra. Despite various efforts, such algebra hasn't been found. In this talk, I will show how promoting such numerators to string level would help tackle this problem. In string theory, BCJ numerators can be written as the vacuum expectation value of some successive skewed commutators of vertex operators. And field theory limit of this algebra contains the diffeomorphism algebra as a truncation and leads to a well behaved field theory numerator.