  Conformally invariant massless field systems involving only dimensionless
parameters are known to describe particle physics at very high energy. In the
presence of an external gravitational field, the conformal symmetry may
generalize to Weyl invariance. However, the latter symmetry no longer survives
after quantization: A Weyl anomaly appears. In this Letter, a purely algebraic
understanding of the universal structure of the Weyl anomalies is presented.
The results hold in arbitrary dimensions and independently of any
regularization scheme.
