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Multi-parameter Quantum Groups related to link-diagrams

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Abstract

We apply the Faddeev-Reshetikhin-Taktajan method for the construction of Quantum Groups to the Yang-Baxter matrices which are related to the invariants of oriented links in Σ×[0,1], where Σ is a non-trivial 2-dimensional surface. We obtain multi-parameter ribbon Hopf algebras that differ in many respects from their one-parameter counterparts. Among the main differences we mention the existence of a non-central quantum determinant and the fact that the number of independent generators is higher than in the one-parameter case.

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Communicated by N. Yu. Reshetikhin

Supported in part by the Italian National Institute for Nuclear Physics (I.N.F.N.) and by the National Science Foundation (N.S.F.) under Grant DMS 89-01975 and Grant DMS/PHY 88-16214

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Cotta-Ramusino, P., Rinaldi, M. Multi-parameter Quantum Groups related to link-diagrams. Commun.Math. Phys. 142, 589–604 (1991). https://doi.org/10.1007/BF02099102

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