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Generalized quantum statistics such as para-Fermi statistics is characterizedby certain triple relations which, in the case of para-Fermi statistics, arerelated to the orthogonal Lie algebra B_n=so(2n+1). In this paper, we give aquite general definition of ``a generalized quantum statistics associated to aclassical Lie algebra G''. This definition is closely related to a certainZ-grading of G. The generalized quantum statistics is then determined by a setof root vectors (the creation and annihilation operators of the statistics) andthe set of algebraic relations for these operators. Then we give a completeclassification of all generalized quantum statistics associated to theclassical Lie algebras A_n, B_n, C_n and D_n. In the classification, severalnew classes of generalized quantum statistics are described

A classification of generalized quantum statistics associated with classical Lie algebras