  Generalized quantum statistics, such as paraboson and parafermion statistics,
are characterized by triple relations which are related to Lie (super)algebras
of type B. The correspondence of the Fock spaces of parabosons, parafermions as
well as the Fock space of a system of parafermions and parabosons to
irreducible representations of (super)algebras of type B will be pointed out.
Example of generalized quantum statistics connected to the basic classical Lie
superalgebra B(1|1)=osp(3|2) with interesting physical properties, such as
noncommutative coordinates, will be given. Therefore the article focuses on the
question, addressed already in 1950 by Wigner: do the equation of motion
determine the quantum mechanical commutation relation?
