Algebraic generalization of quantum statistics

Generalized quantum statistics such as para-Bose and para-Fermi statistics are related to the basic classical Lie superalgebras B(0|n) and B_n. We give a quite general definition of 'a generalized quantum statistics associated to a Lie superalgebra G'. This definition is closely related to a certain Z-grading of G. The generalized quantum statistics is determined by a set of root vectors (the creation and annihilation operators of the statistics) and the set of algebraic relations for these operators. Then we give a complete classification of all generalized quantum statistics associated to the Lie superalgebras A_n, B_n, C_n, D_n, G₂, F₄, E₆, E₇, E₈, A(m|n), B(m|n), C(n), D(m|n), G(3), F(4) and D(2; 1; α).