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A classification of generalized quantum statistics associated with classical Lie algebras

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

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.

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N. I. Stoilova, J. Van der Jeugt. 2004-09-01. A classification of generalized quantum statistics associated with classical Lie algebras. https://doi.org/10.1063/1.1827324

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