The quantum de Rham complexes associated with $S{L}_h(2)$

Abstract

Quantum de Rham complexes on the quantum plane and the quantum group itself are constructed for the Zakrewski deformation of $Fun(SL(2))$. As a by-product a new deformation of the two dimensional Heisenberg algeb ra is constructed which can be used to construct models of h-deformed quantum mechanics.

15 pages

References in corpus (1)

• Differential Geometry on Linear Quantum Groups

Cited by in corpus (18)

• $h$-Deformation as a Contraction of $q$-Deformation
• h-deformation of GL(1|1)
• Deformed and extended Galilei group Hopf algebras
• Boson representations, non-standard quantum algebras and contractions
• Duality for the Jordanian Matrix Quantum Group $G{L}_{g,h}(2)$
• Deformed Minkowski spaces: clasification and properties
• Bicovariant Differential Geometry of the Quantum Group $S{L}_h(2)$
• The Jordanian deformation of su(2) and Clebsch-Gordan coefficients
• Generalization of the $h$-Deformation to Higher Dimensions
• Representation Functions for Jordanian Quantum Group SL_h(2) and Jacobi Polynomials
• Classification of bicovariant differential calculi on the Jordanian quantum groups GL_{g,h}(2) and SL_{h}(2) and quantum Lie algebras
• Two-parameter differential calculus on the h-superplane
• Symplecton for U_h(sl(2)) and representations of SL_h(2)
• h-deformation of Gr(2)
• Quantum Gauge Theories
• Maps between Deformed and Ordinary Gauge Fields
• Two-parameter nonstandard deformation of 2x2 matrices
• Two-Parameter Differential Calculus on the h-Exterior Plane