Classification of three-dimensional linear Nijenhuis operators with functionally independent invariants

The paper contains solution of the problem of classification of three-dimensional left-symmetric algebras satisfying the following additional condition: the coefficients of the characteristic polynomial of the operator $L^i_k(x)= \sum a^i_{ks}x^s$, where $a^i_{ks}$ are the structural constants of the algebra, are functionally independent polynomials of $x^1,\dots, x^n$.