Contraction of the Gr,s quantum group to its nonstandard analog and corresponding colored quantum groups

DOI10.1063/1.533248zbMath0973.81052arXivmath/9911194OpenAlexW2031205471MaRDI QIDQ2737941

Roger McDermott, Deepak Parashar

Publication date: 30 August 2001

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9911194

zbMATH Keywords

Jordanian quantum group

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50)

Related Items (2)

On the biparametric quantum deformation of GL(2)⊗GL(1) ⋮ The coloured quantum plane

Cites Work

• A Hopf star-algebra of polynomials on the quantum \(SL(2,\mathbb{R})\) for a `unitary' \(R\)-matrix
• A \(*\)-product on SL(2) and the corresponding nonstandard quantum- U\(({\mathfrak sl}(2))\)
• Jordanian \(U_{h,s}gl(2)\) and its coloured realization
• \(h\)-deformation of GL\((1| 1)\)
• THE TWO-PARAMETRIC EXTENSION OF h DEFORMATION OF GL(2), AND THE DIFFERENTIAL CALCULUS ON ITS QUANTUM PLANE
• IRREDUCIBLE REPRESENTATIONS OF JORDANIAN QUANTUM ALGEBRA U_h(sl(2)) VIA A NONLINEAR MAP
• THE UNIVERSAL R-MATRIX FOR THE JORDANIAN DEFORMATION OF sl(2), AND THE CONTRACTED FORMS OF so(4)
• INHOMOGENEOUS QUANTUM GROUPS IGL_q,r(N): UNIVERSAL ENVELOPING ALGEBRA AND DIFFERENTIAL CALCULUS
• COLORED EXTENSIONS OF GL_q(2) QUANTUM GROUP AND RELATED NONCOMMUTATIVE PLANES
• The quantum group GL_h(2)
• Generalization of the h-deformation to higher dimensions
• Colored quantum universal enveloping algebras
• UniversalR-matrix for non-standard quantum
• Jordanian deformation of SL(2) as a contraction of its Drinfeld-Jimbo deformation

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