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

N. I. Stoilova·J. Van der Jeugt
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Abstract

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 B_n=so(2n+1); in the case of para-Bose 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).

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N. I. Stoilova, J. Van der Jeugt. 2005-04-05. A classification of generalized quantum statistics associated with basic classical Lie superalgebras. https://doi.org/10.1063/1.2104287

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