Generalized statistics and the algebra of observables

A short review is given of how to apply the algebraic Heisenberg quantization scheme to a system of identical particles. For two particles in one dimension the approach leads to a generalization of the Bose and Fermi description which can be expressed in the form of a 1/x^2 statistics interaction between the particles. For an N-particle system it is shown how a particular infinite-dimensional algebra arises as a generalization of the su(1,1) algebra which is present for the two-particle system.