  In this note we want to have another look on Schwinger-Dyson equations for
the eigenvalue distributions and the fluctuations of classical unitarily
invariant random matrix models. We are exclusively dealing with one-matrix
models, for which the situation is quite well understood. Our point is not to
add any new results to this, but to have a more algebraic point of view on
these results and to understand from this perspective the universality results
for fluctuations of these random matrices. We will also consider corresponding
non-commutative or "quantum" random matrix models and contrast the results for
fluctuations and Schwinger-Dyson equations in the quantum case with the
findings from the classical case.
