Multiparameter Quantum Groups and Multiparameter R-Matrices

Michiel Hazewinkel
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Michiel Hazewinkel: CWI

A chapter in Geometric and Algebraic Structures in Differential Equations, 1995, pp 57-98 from Springer

Abstract: 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.

Keywords: Commutation Relation; Quantum Group; Braid Group; Laurent Polynomial; Quantum Space (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0179-7_5

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DOI: 10.1007/978-94-009-0179-7_5

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