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Universal $R$--matrices for non-standard (1+1) quantum groups

A. Ballesteros·E. Celeghini·F. J. Herranz·M. A. del Olmo·M. Santander
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Abstract

A universal quasitriangular $R$--matrix for the non-standard quantum (1+1) Poincar\'e algebra $U_ziso(1,1)$ is deduced by imposing analyticity in the deformation parameter $z$. A family $g_\mu$ of ``quantum graded contractions" of the algebra $U_ziso(1,1)\oplus U_{-z}iso(1,1)$ is obtained; this set of quantum algebras contains as Hopf subalgebras with two primitive translations quantum analogues of the two dimensional Euclidean, Poincar\'e and Galilei algebras enlarged with dilations. Universal $R$--matrices for these quantum Weyl algebras and their associated quantum groups are constructed.

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A. Ballesteros, E. Celeghini, F. J. Herranz, M. A. del Olmo, M. Santander. 1995-01-27. Universal $R$--matrices for non-standard (1+1) quantum groups. https://doi.org/10.1088/0305-4470%2F28%2F11%2F015

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