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[ **DEFORMED HEISENBERG ALGEBRA,\
FRACTIONAL SPIN FIELDS\
AND\
SUPERSYMMETRY WITHOUT FERMIONS**]{}\
1.0cm [ **Mikhail S. Plyushchay[^1]** ]{}\
[*Departamento de Física Teórica, Facultad de Ciencias*]{}\
[*Universidad de Zaragoza, Zaragoza 50009, Spain*]{}\
[**Annals of Physics 245 (1996) 339-360**]{}

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[**Abstract**]{}

Within a group-theoretical approach to the description of (2+1)-dimensional anyons, the minimal covariant set of linear differential equations is constructed for the fractional spin fields with the help of the deformed Heisenberg algebra (DHA), $[a^{-},a^{+}]=1+\nu K$, involving the Klein operator $K$, $\{K,a^{\pm}\}=0$, $K^{2}=1$. The connection of the minimal set of equations with the earlier proposed ‘universal’ vector set of anyon equations is established. On the basis of this algebra, a bosonization of supersymmetric quantum mechanics is carried out. The construction comprises the cases of exact and spontaneously broken $N=2$ supersymmetry allowing us to realize a Bose-Fermi transformation and spin-1/2 representation of SU(2) group in terms of one bosonic oscillator. The construction admits an extension to the case of OSp(2$\vert$2) supersymmetry, and, as a consequence, both applications of the DHA turn out to be related. A possibility of ‘superimposing’ the two applications of the DHA for constructing a supersymmetric (2+1)-dimensional anyon system is discussed. As 