  For the chiral oscillator described by a second order and degenerate
Lagrangian with special Euclidean group of symmetries, we show, by cotangent
bundle Hamiltonian reduction, that reduced equations are Lie-Poisson on dual of
oscillator algebra, the central extension of special Euclidean algebra in two
dimensions. This extension, defined by symplectic two-cocycle of special
Euclidean algebra, seems to be an enforcement of reduction itself rooted to
Casimir function.
