We discuss a relativistic free particle with fractional spin in 2+1 di
mensions, where the dual spin components satisfy the canonical angular
momentum algebra {S-mu, S-upsilon} = epsilon(mu upsilon gamma)S(gamma
). It is shown that it is a general consequence of these features that
the Poincare invariance is broken down to the Lorentz one, so indicat
ing that it is not possible to keep simultaneously the free nature of
the anyon and the translational invariance.