**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.*

ruthel@ma.huji.ac.il