  We discuss the connection between anyons (particles with fractional
statistics) and deformed Lie algebras (quantum groups). After a brief review of
the main properties of anyons, we present the details of the anyonic
realization of all deformed classical Lie algebras in terms of anyonic
oscillators. The deformation parameter of the quantum groups is directly
related to the statistics parameter of the anyons. Such a realization is a
direct generalization of the Schwinger construction in terms of fermions and is
based on a sort of bosonization formula which yields the generators of the
deformed algebra in terms of the undeformed ones. The entire procedure is well
defined on two-dimensional lattices, but it can be consistently reduced also to
one-dimensional chains.
