A classification of generalized quantum statistics associated with basic classical Lie superalgebras

Generalized quantum statistics such as para-statistics is usually characterized by certain triple relations. In the case of para-Fermi statistics these relations can be associated with the orthogonal Lie algebra Bn = so(2n + 1); in the case of paraBose statistics they are associated with the Lie superalgebra B(0|n) = osp(1|2n). In a previous paper, a mathematical definition of “a generalized quantum statistics associated with a classical Lie algebra G” was given, and a complete classification was obtained. Here, we consider the definition of “a generalized quantum statistics associated with a basic classical Lie superalgebra G”. Just as in the Lie algebra case, this definition is closely related to a certain Z-grading of G. We give in this paper a complete classification of all generalized quantum statistics associated with the basic classical Lie superalgebras A(m|n), B(m|n), C(n) and D(m|n). Running title: Classification of generalized statistics PACS: 02.20.+b, 03.65.Fd, 05.30-d. Permanent address: Institute for Nuclear Research and Nuclear Energy, Boul. Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria