Interpretation and Extension of the Green's Ansatz for Paraparticles

The anomalous bilinear commutation relations satisfied by the components of the Green's ansatz for paraparticles are shown to derive from the comultiplication of the paraboson or parafermion algebra. The same provides a generalization of the ansatz, wherein paraparticles of order $p=\sum_{\alpha=1}^r p_{\alpha}$ are constructed from r paraparticles of order $p_{\alpha}$, $\alpha$=1,2, ...,r.