Classes of f-Deformed Landau Operators: Nonlinear Noncommutative Coordinates from Algebraic Representations

1); (2) CP3; 3; (3) Fellow; Belgium; Cotonou; Jan Govaerts (2; Joseph Ben Geloun (1); Louvain-la-Neuve; M. N. Hounkonnou (1) ((1) ICMAP

arxiv: 0812.0725 · v1 · submitted 2008-12-03 · ✦ hep-th

Classes of f-Deformed Landau Operators: Nonlinear Noncommutative Coordinates from Algebraic Representations

Joseph Ben Geloun (1) , Jan Govaerts (2 , 3 , 1) , M. N. Hounkonnou (1) ((1) ICMAP , Cotonou , Rep. Benin , (2) CP3

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UCL Louvain-la-Neuve Belgium (3) Fellow Stellenbosch Institute for Advanced Study Stellenbosch Rep. South Africa)

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classification ✦ hep-th

keywords algebrasclassesf-deformedlandaunoncommutativenonlinearoperatorsalgebra

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We consider, in a superspace, new operator dependent noncommutative (NC) geometries of the nonlinear quantum Hall limit related to classes of f-deformed Landau operators in the spherical harmonic well. Different NC coordinate algebras are determined using unitary representation spaces of Fock-Heisenberg tensored algebras and of the Schwinger-Fock realisation of the su(1,1) Lie algebra. A reduced model allowing an underlying N=2 superalgebra is also discussed.

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Classes of f-Deformed Landau Operators: Nonlinear Noncommutative Coordinates from Algebraic Representations

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