  An algebraic formalism for description of quantum states of charged particle
with spin moving in two-dimensional space under influence of singular magnetic
field is developed in terms of graded algebras. The fundamental assumption is
that the particle is transformed into a composite system which consists
quasiparticles, quasiholes and magnetic fluxes. Such system is endowed with
generalized statistics determined by a grading group and a commutation factor
on it. Composite systems corresponding to the quantum Hall effect and the
electronic magnetotransport anomaly are described. The Fock space
representation are also given.
