  We discuss a relativistic free particle with fractional spin in 2+1
dimensions, where the dual spin components satisfy the canonical angular
momentum algebra $\left\{ S_\mu , S_\nu \right\}\,=\,\epsilon_{\mu \nu
\gamma}S^\gamma $. It is shown that it is a general consequence of these
features that the Poincar\`e invariance is broken down to the Lorentz one, so
indicating that it is not possible to keep simultaneously the free nature of
the anyon and the translational invariance.
