  Generalized quantum statistics such as para-Fermi statistics is characterized
by certain triple relations which, in the case of para-Fermi statistics, are
related to the orthogonal Lie algebra B_n=so(2n+1). In this paper, we give a
quite general definition of ``a generalized quantum statistics associated to a
classical Lie algebra G''. This definition is closely related to a certain
Z-grading of G. The generalized quantum statistics is then 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
classical Lie algebras A_n, B_n, C_n and D_n. In the classification, several
new classes of generalized quantum statistics are described.
