Universal Link Invariants using Quantum Groups

R.J. Lawrence

Abstract: Until now there have been many methods for obtaining the generalised Jones invariants of knots and links, but all have had as given data, a Lie group together with a representation. In this paper we shall show how to obtain link invariants lying in the tensor power of a quotient of a quantum group, which reduce to projections of the known Jones invariants when a representation is given. Such link invariants exist for each quantum group equipped with a solution of the Yang-Baxter equation and thus, in particular, for any quantum group obtained by quantising a Lie group.

Keywords: Knot theory, Jones polynomial, quantum group, R-matrix, Yang-Baxter equation, braid group representation.

AMS subject classification: 57M25 17B37

Length: 9 pages

Reference: `Proceedings of the XVII Int. Conf. on Differential Geometric Methods in Theoretical Physics, Chester, England, 15th-19th August, 1988.' Ed. A. Solomon, World Scientific (1989) 55-63. MR1124415 (92e:57012)

Last updated on September 4th, 1996.