Representations of correlations of the $і [A, B] = f(A) + g(B)$ type - Samoilenko , Yu. S.; Shulman , V. S. (Ukrains’kyi Matematychnyi Zhurnal, 1991)
It is proved that all nontrivial representations of quadratic relation $i [A, B] = f(A) + g(B)$ 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 $II_I$, but can have infinite-dimensional irreducible representations with bounded operators.