Abstract
There exists an ( n2 ) + 1 parameter quantum group deformation of GLn which has been constructed independently by several (groups of) authors. In this note, I give an explicitR-matrix for this multiparameter family. This gives additional information on the nature of this family and facilitates some calculations. This explicitR-matrix satisfies the Yang-Baxter equation. The centre of the paper is Section 3 which describes all solutions of the YBE under the restriction r abcd =0 unlessa, b=c, d. One kind of the most general constituents of these solutions precisely corresponds to the ( n2 ) + 1 parameter quantum group mentioned above. I describe solutions which extend to an enhanced Yang-Baxter operator and, hence, define link invariants. The paper concludes with some preliminary results on these link invariants.
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Hazewinkel, M. Multiparameter quantum groups and multiparameterR-matrices. Acta Appl Math 41, 57–98 (1995). https://doi.org/10.1007/BF00996106
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DOI: https://doi.org/10.1007/BF00996106