A classification of generalized quantum statistics associated with the exceptional Lie (super)algebras

Details A classification of generalized quantum statistics associated with the exceptional Lie (super)algebras A classification of generalized quantum statistics associated with the exceptional Lie (super)algebras

2006-11-30

arxiv.org/abs/math-ph/0611085v1

J. Math. Phys. 48, 043504 (2007)

Physics

Mathematical Physics

22 pages

Scientific paper

10.1063/1.2712914

Generalized quantum statistics (GQS) associated to a Lie algebra or Lie superalgebra extends the notion of para-Bose or para-Fermi statistics. Such GQS have been classified for all classical simple Lie algebras and basic classical Lie superalgebras. In the current paper we finalize this classification for all exceptional Lie algebras and superalgebras. Since the definition of GQS is closely related to a certain Z-grading of the Lie (super)algebra G, our classification reproduces some known Z-gradings of exceptional Lie algebras. For exceptional Lie superalgebras such a classification of Z-gradings has not been given before.

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