Ladder operators, Fock-spaces, irreducibility and group gradings for the Relative Parabose Set algebra

zbMath1246.81056arXiv1006.4120MaRDI QIDQ2901369

Alfredo Herrera-Aguilar, Konstantinos Kanakoglou

Publication date: 20 July 2012

Full work available at URL: https://arxiv.org/abs/1006.4120

zbMATH Keywords

representationssimple modulesirreducibilityladder operatorsgenerators and relationsgradingparaparticlesFockrelative parabose set

Mathematics Subject Classification ID

Color Lie (super)algebras (17B75) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Many-body theory; quantum Hall effect (81V70) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Operator algebra methods applied to problems in quantum theory (81R15) Graded rings and modules (associative rings and algebras) (16W50) Computational aspects of associative rings (general theory) (16Z05)

Related Items (6)

The Z2×Z2 -graded Lie superalgebras pso(2n+1|2n) and pso(∞|∞) , and parastatistics Fock spaces ⋮ Representations of the Lie superalgebra $ \newcommand{\B}{\mathfrak{B}} {\B(\infty,\infty)}$ and parastatistics Fock spaces ⋮ Gradings, braidings, representations, paraparticles: some open problems ⋮ The $ \newcommand{\Z}{{{\mathbb Z}}} \Z_2\times\Z_2$ -graded Lie superalgebra $ \newcommand{\pso}{\mathfrak{pso}} \pso(2m+1\vert 2n)$ and new parastatistics representations ⋮ Z2×Z2 -graded parastatistics in multiparticle quantum Hamiltonians ⋮ Inequivalent quantizations from gradings and Z2×Z2 parabosons

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