The 2-Parametric Extension of $h$ Deformation of $GL(2)$, and The Differential Calculus on Its Quantum Plane

Abstract

We present an alternative 2-parametric deformation $GL(2{)}_{h,h^{\prime }}$ , and construct the differential calculus on the quantum plane on which this quantum group acts. Also we give a new deformation of the two dimensional Heisenberg algebra

11 pages, Institute for studies in Theoretical Physics and Mathematics Tehran Iran

Cited by in corpus (29)

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• Noncommutative Geometry of the h-deformed Quantum Plane
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• Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits
• Duality for the Jordanian Matrix Quantum Group $G{L}_{g,h}(2)$
• Spectral Decomposition and Baxterisation of Exotic Bialgebras and Associated Noncommutative Geometries
• On Jordanian U_{h,α}(gl(2)) Algebra and Its T Matrices Via a Contraction Method
• Propagator on the h-deformed Lobachevsky plane
• Quantum Mechanics on the h-deformed Quantum Plane
• Duality for Exotic Bialgebras
• Duality and Representations for New Exotic Bialgebras
• The Jordanian deformation of su(2) and Clebsch-Gordan coefficients
• Generalization of the $h$-Deformation to Higher Dimensions
• Bicovariant Differential Geometry of the Quantum Group $S{L}_h(2)$
• Representation Functions for Jordanian Quantum Group SL_h(2) and Jacobi Polynomials
• Drinfeld twist for two-parametric deformation of gl(2) and sl(1/2)
• Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups
• Two-parameter differential calculus on the h-superplane
• RTT relations, a modified braid equation and noncommutative planes
• Jordanian quantum spheres
• h-deformation of Gr(2)
• Automorphisms of associative algebras and noncommutative geometry
• On a "New" Deformation of GL(2)
• Maps between Deformed and Ordinary Gauge Fields
• The coloured quantum plane
• Realisations of Quantum GL_p,q(2) and Jordanian GL_h,h'(2)
• Two-Parameter Differential Calculus on the h-Exterior Plane