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

Journal Article · Sun Apr 15 00:00:00 EDT 2007 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2712914· OSTI ID:20929686

Stoilova, N I; Jeugt, J van der ^[1]

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1. Department of Applied Mathematics and Computer Science, University of Ghent, Krijgslaan 281-S9, B-9000 Gent (Belgium)

Generalized quantum statistics (GQS) associated with 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.

• OSTI ID: 20929686
• Journal Information: Journal of Mathematical Physics, Vol. 48, Issue 4; Other Information: DOI: 10.1063/1.2712914; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
BOSONS
CLASSIFICATION
FERMI STATISTICS
FERMIONS
GRADED LIE GROUPS
QUANTUM MECHANICS
STATISTICS