Vestnik of Samara University. Natural Science SeriesVestnik of Samara University. Natural Science Series2541-75252712-8954Samara National Research University444510.18287/2541-7525-2015-21-10-9-23U -projection for the adjoint representation of the groupGL( n, K)VyatkinaK.A.morenov.sv@ssau.ru1510201521109231505201715052017Copyright © 2015, Vyatkina K.2015In the paper we study rings and fields of invariants for the adjoint represen- tation of the group GL(n, K) over the field of zero characteristic. The aim of this paper is to construct the special linear operator, we call it U -projector, that maps any polynomial on the matrix algebra to an U -invariant rational function. In this paper we present two different constructions of U -projector. Using the U -projector we obtain the system of generators of the field of U -invariants of the adjoint representation of the group GL(n, K). We obtain the system of genera- tors of the field of U -invariants for the restriction of the adjoint representation to the subgroup of block-diagonal matrices.field of invariants, adjoint representation, unitriangular group, solvable group, algebra of invariants, representations of groups, locally nilpotent derivation, system of generators.поле инвариантовприсоединенное представлениеунитреугольная группаразрешимая группаалгебра инвариантовпредставления групплокально нильпотентное дифференцированиесистема образующих элементов