Extended Weyl-Heisenberg algebra and Rubakov-Spiridonov superalgebra: Anyonic realizations

We give the realizations of the extended Weyl-Heisenberg (WH) algebra and the Rubakov-Spiridonov (RS) superalgebra in terms of anyons, characterized by the statistical parameter $\nu \in [0,1]$, on two-dimensional lattice. The construction uses anyons defined from usual fermionic oscillators (Lerda-Sciuto construction). The anyonic realization of the superalgebra $sl(1\mathrm{/}1)$ is also presented.