Representations of relations of the form i[A,B]=f(A)+G(B)

It is proved that all nontrivial representations of quadratic relation iA, B]=f(A)+g(B) with self-adjoint operators A, B are unbounded if f and g are nonnegative; for any f and g this relation does not have nontrivial finite-dimensional representations and factor-representations of type II₁, but can have infinite-dimensional irreducible representations with bounded operators.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 1, pp. 110–114, January, 1991.