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Multiparameter Quantum Groups and Multiparameter R-Matrices

In: Geometric and Algebraic Structures in Differential Equations

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  • Michiel Hazewinkel

    (CWI)

Abstract

There exists an ( 2 n ) + 1 parameter quantum group deformation of GL n which has been constructed independently by several (groups of) authors. In this note, I give an explicit R-matrix for this multiparameter family. This gives additional information on the nature of this family and facilitates some calculations. This explicit R-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 cd ab = 0 unless {a, b} = {c, d}. One kind of the most general constituents of these solutions precisely corresponds to the ( 2 n ) + 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.

Suggested Citation

  • Michiel Hazewinkel, 1995. "Multiparameter Quantum Groups and Multiparameter R-Matrices," Springer Books, in: P. H. M. Kersten & I. S. Krasil’Shchik (ed.), Geometric and Algebraic Structures in Differential Equations, pages 57-98, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-0179-7_5
    DOI: 10.1007/978-94-009-0179-7_5
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