ISSN:
1572-9036
Keywords:
16W30
;
58F07
;
57M25
;
multiparameter quantum group
;
multiparameterR-matrix
;
Yang-Baxter equation
;
Hopf algebra
;
bialgebra
;
PBW-algebra
;
knot invariant
;
link invariant
;
confluent rewriting system
;
fundamental communication relations (FCR)
;
diamond lemma
;
generalized quantum space
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract There exists an ( 2 n ) + 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 cd ab =0 unlessa, 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00996106
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