Boson, para-boson, and boson-fermion representations of some graded Lie algebras

DOI10.1063/1.524764zbMath0474.22012OpenAlexW2058459659MaRDI QIDQ3929946

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Publication date: 1981

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.524764

zbMATH Keywords

matrix representationmatrix elementsBose sectorscreation and annihilation operatorgenerators of graded Lie algebras

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70) Axiomatic quantum field theory; operator algebras (81T05) Superalgebras (17A70) Graded Lie (super)algebras (17B70) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Representations of group algebras (22D20)

Cites Work

• Graded Lie algebras in mathematics and physics (Bose-Fermi symmetry)
• A classification of four-dimensional Lie superalgebras
• Generalized Lie algebras
• Fourth degree Casimir operator of the semisimple graded Lie algebra (Sp(2N); 2N)
• Erratum: Semisimple Lie algebras
• Classification of all simple graded Lie algebras whose Lie algebra is reductive. I
• Elementary construction of graded Lie groups
• Simple supersymmetries
• Irreducible Representations of Generalized Oscillator Operators
• On non-compact groups I. Classification of non-compact real simple Lie groups and groups containing the Lorentz group
• A Generalized Method of Field Quantization
• Lie superalgebras

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