  We show that the Bessel equation can be cast, by means of suitable
transformations, into a system of two damped/amplified parametric oscillator
equations. The relation with the group contraction mechanism is analyzed and
the breakdown of loop-antiloop symmetry due to group contraction manifests
itself as violation of time-reversal symmetry. A preliminary discussion of the
relation between some infinite dimensional loop-algebras, such as the
Virasoro-like algebra, and the Euclidean algebras e(2) and e(3) is also
presented.
