Multi-Species Anyons Supersymmetry on Two-Dimensional Space

The algebra of multi-species anyons characterized by different statistical parameters $\nu_{ij}=e_{i}e_{j}\Phi_{i}\Phi_{j}/(2\pi)$, $i,j=1,...,n$ is redefined by basing on fermions and $k_{i}$-fermions ($k_{i}\in\bf{N}\rm /\{0,1\}$ with $i\in\bf{N}\rm$) and its superalgebra is constructed. The so-called fractional supersymmetry of multi-species anyons is realized on 2d lattice.