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Strongly spin-preserving solutions of the Yang-Baxter equation and their link invariants

Published online by Cambridge University Press:  24 October 2008

M. A. Hennings
M. A. Hennings
Affiliation:
Sidney Sussex College, Cambridge, CB2 3HU
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Extract

Recently Kauffman[2, 3] has classified the (strongly) spin-preserving solutions of the Yang—Baxter equation, and in particular discussed two solutions. One of these can be used to obtain the Jones polynomial, while the other (with care) leads to the Alexander polynomial. In this paper we shall complete this analysis, and shall describe all strongly spin-preserving invertible solutions of the Yang-Baxter equation which lead to link invariants. Having done this, we investigate what sort of link invariants can be obtained from these solutions. It turns out that these invariants are precisely those which have been described in Hennings [l].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 113 , Issue 2 , March 1993 , pp. 401 - 411
Copyright
Copyright © Cambridge Philosophical Society 1993

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References

REFERENCES

[1]Hennings, M. A.. A polynomial invariant for oriented banded links. Preprint (1989).Google Scholar
[2]Kauffman, L. H.. Knots, abstract tensors and the Yang-Baxter equation. In Knots, Topology and Quantum Field Theories. Proceedings of the Johns Hopkins Workshop on Current Problems in Particle Theory 13 (editor Lussana, L.), (World Scientific, 1989), pp. 179–334.Google Scholar
[3]Kauffmas, L. H.. Knots and Physics. Series on Knots and Everything (World Scientific, 1991).Google Scholar