The universal R-matrix for the Jordanian deformation of sl(2), and the contracted forms of so(4)

Abstract

We introduce a universal R matrix for the Jordanian deformation of $\U{ \sl(2)}$. Using $\Uh{\so(4)}=\Uh{\sl(2)} \oplus {\rm U}_{-h}(\sl(2))$, we obtain the universal R matrix for $\Uh{\so(4)}$. Applying the graded contractions on the universal R matrix of $\Uh{\so(4)}$, we show that there exist three distinct R matrices for all of the contracted algebras. It is shown that $\Uh{\sl(2)}$, $\Uh{\so(4)}$, and all of these contracted algebras are triangular.

LaTeX, 8 pages

Cited by in corpus (18)

• Universal $R$-matrix for non-standard quantum $sl(2,\mathbb{R})$
• (1+1) Schrodinger Lie bialgebras and their Poisson-Lie groups
• Null-plane Quantum Universal $R$-matrix
• Boson representations, non-standard quantum algebras and contractions
• 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
• Twist maps for non-standard quantum algebras and discrete Schrodinger symmetries
• Poisson-Hopf algebra deformations of Lie-Hamilton systems
• Coloured quantum universal enveloping algebras
• The Twisted Heisenberg Algebra ${\mathcal{U}}_{h,w}(\mathcal{H}(4))$
• New time-type and space-type non-standard quantum algebras and discrete symmetries
• Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups
• Tensor Operators for Uh(sl(2))
• Nonstandard Poincare and Heisenberg Algebras
• Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups
• A general approach to noncommutative spaces from Poisson homogeneous spaces: Applications to (A)dS and Poincaré
• Realisations of Quantum GL_p,q(2) and Jordanian GL_h,h'(2)