Abstract
The purpose of this note is to give a complete description of all invertible solutions of the Yang-Baxter equations on \(V \otimes V \) that are of the formσ+ Pwhere a is the flip andPis a rank one tarnsformation. The main result is that the corresponding variety has dimension \({{n}^{2}} + \left[ {\frac{n}{2}} \right] \) with n=dim V. The solutions are shown to give special values of the Jones polynomial of knot theory (in fact give a very elementary proof of its existence) and to give representations of the Temperley-Lieb algebra.
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References
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Wallach, N.R. (1999). A Variety of Solutions to the Yang-Baxter Equation. In: Brylinski, JL., Brylinski, R., Nistor, V., Tsygan, B., Xu, P. (eds) Advances in Geometry. Progress in Mathematics, vol 172. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1770-1_17
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DOI: https://doi.org/10.1007/978-1-4612-1770-1_17
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