Classification of Three-Dimensional Linear Nijenhuis Operators with Functionally Independent Invariants

The paper contains solution to the problem of classification of three-dimensional left-symmetric algebras satisfying the following additional condition: the coefficients of the characteristic polynomial for 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 \(x^{1},\dots,x^{n}\) .