FACTORIZATION PROBLEM WITH INTERSECTION

We propose a generalization of the factorization method to the case when g is a finite-dimensional Lie algebra g = g(0) circle plus M circle plus N (direct sum of vector spaces), where g(0) is a subalgebra in g, M, N are g(0)-modules, and g(0) + M, g(0) + N are subalgebras in g. In particular, our construction involves the case when g is a Z-graded Lie algebra. Using this generalization, we construct certain top-like systems related to algebra so(3, 1). According to the general scheme, these systems can be reduced to solving systems of linear equations with variable coefficients. For these systems we find polynomial first integrals and infinitesimal symmetries.