$h$-Deformation as a Contraction of $q$-Deformation

Abstract

We show that $h$-deformation can be obtained, by a singular limit of a similarity transformation, from $q$-deformation; to be specefic, we obtain $\GL_h(2)$, its differential structure, its inhomogenous extension, and $\Uh{\sl(2)}$ from their $q$-deformed counterparts.

6 pages, LaTeX, IPM-94-61

References in corpus (4)

• Differential Geometry on Linear Quantum Groups
• The 2-Parametric Extension of $h$ Deformation of $GL(2)$, and The Differential Calculus on Its Quantum Plane
• The quantum de Rham complexes associated with $S{L}_h(2)$
• A Closed Expression for the Universal R-Matrix in a Non-Standard Quantum Double

Cited by in corpus (33)

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• Deformed and extended Galilei group Hopf algebras
• Noncommutative Geometry of the h-deformed Quantum Plane
• Multiparametric quantum gl(2): Lie bialgebras, quantum R-matrices and non-relativistic limits
• Irreducible decomposition for tensor prodect representations of Jordanian quantum algebras
• General Construction of Nonstandard $R_h$-matrices as Contraction Limits of $R_q$-matrices
• Deformed Minkowski spaces: clasification and properties
• On Jordanian U_{h,α}(gl(2)) Algebra and Its T Matrices Via a Contraction Method
• Coloured quantum universal enveloping algebras
• The Twisted Heisenberg Algebra ${\mathcal{U}}_{h,w}(\mathcal{H}(4))$
• Bicovariant differential calculus on the superspace ${\mathbb{R}}_q(1|2)$
• Generalization of the $h$-Deformation to Higher Dimensions
• Covariant Differential Calculi on $S{P}_q^{1|2}$
• Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups
• The Hopf algebra structure of the Z${}_3$-graded quantum supergroup GL${}_{q,j}(1|1)$
• Jordanian Quantum Algebra ${\mathcal{U}}_{\mathsf{h}}(sl(N))$ via Contraction Method and Mapping
• Tensor Operators for Uh(sl(2))
• On $q$- and $h$-deformations of 3d-superspace
• Quantum de Rham complex on ${\mathbb{A}}_h^{1|2}$
• h-deformation of Gr(2)
• Differential geometry of GL${}_h(1|1)$
• Maps between Deformed and Ordinary Gauge Fields
• The coloured quantum plane
• Quantum harmonic oscillator algebras as non-relativistic limits of multiparametric $gl(2)$ quantizations
• On the biparametric quantum deformation of GL(2) x GL(1)
• Properties of $2\times 2$ h-deformed quantum (super)matrices
• A Differential Calculus on the $(h,j)$-Deformed Z${}_3$-Graded Superplane
• Hopf algebra structure on symplectic superspace ${\mathrm{SP}}_q^{2|1}$
• Realisations of Quantum GL_p,q(2) and Jordanian GL_h,h'(2)
• Inhomogeneous Multiparameter Jordanian Quantum Groups by Contraction
• Two-parameter nonstandard deformation of 2x2 matrices