he factor-algebras A\I are regarded where A is a free associative algebra the universally enveloping algebra of a finitely dimential Lie algebra over a field of zero characteristic and I an ideal of A generated by a finite Groebner-Shirshov basis. It is proved that the property of A\I to by Lie nilpotent algebra(with a fixed index) is algorithmically recognizable.

recognizable properties of algebras, polynomial identities, universally enveloping algebras of the finitely dimential Lie algebras

Mathematical problems and theory of numerical methods