Quantum group and Manin plane related to a coloured braid group representation

Details Quantum group and Manin plane related to a coloured braid group representation Quantum group and Manin plane related to a coloured braid group representation

1993-07-30

arxiv.org/abs/hep-th/9307192v1

Physics

High Energy Physics

High Energy Physics - Theory

20 Pages

Scientific paper

By considering `coloured' braid group representation we have obtained a quantum group, which reduces to the standard $GL_q(2)$ and $GL_{p,q}(2)$ cases at some particular limits of the `colour' parameters. In spite of quite complicated nature, all of these new quantum group relations can be expressed neatly in the Heisenberg-Weyl form, for a nontrivial choice of the basis elements. Furthermore, it is possible to associate invariant Manin planes, parametrised by the `colour' variables, with such quantum group structure.

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