Multiparametric and coloured extensions of the quantum group $GL_q(N)$ and the Yangian algebra $Y(gl_N)$ through a symmetry transformation of the Yang-Baxter equation

Details Multiparametric and coloured extensions of the quantum group $GL_q(N)$ and the Yangian algebra $Y(gl_N)$ through a symmetry transformation of the Yang-Baxter equation Multiparametric and coloured extensions of the quantum group $GL_q(N)$ and the Yangian algebra $Y(gl_N)$ through a symmetry transformation of the Yang-Baxter equation

1995-11-29

arxiv.org/abs/q-alg/9511028v2

Int.J.Mod.Phys. A12 (1997) 945-962

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, LaTeX (twice). Interesting physical applications of the work are indicated. To appear in Int. J. Mod. Phys. A

Scientific paper

10.1142/S0217751X97000700

Inspired by Reshetikhin's twisting procedure to obtain multiparametric extensions of a Hopf algebra, a general `symmetry transformation' of the `particle conserving' $R$-matrix is found such that the resulting multiparametric $R$-matrix, with a spectral parameter as well as a colour parameter, is also a solution of the Yang-Baxter equation (YBE). The corresponding transformation of the quantum YBE reveals a new relation between the associated quantized algebra and its multiparametric deformation. As applications of this general relation to some particular cases, multiparametric and coloured extensions of the quantum group $GL_q(N)$ and the Yangian algebra $Y(gl_N)$ are investigated and their explicit realizations are also discussed. Possible interesting physical applications of such extended Yangian algebras are indicated.

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