Drinfeld-Manin solutions of the Yang-Baxter equation coming from cube complexes

Alina Vdovina

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arXiv · 2007.01163

Drinfeld-Manin solutions of the Yang-Baxter equation coming from cube complexes

Alina Vdovina

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Abstract

The most common geometric interpretation of the Yang-Baxter equation is by braids, knots and relevant Reidemeister moves. So far, cubes were used for connections with the third Reidemeister move only. We will show that there are higher-dimensional cube complexes solving the $D$-state Yang-Baxter equation for arbitrarily large $D$. More precisely, we introduce explicit constructions of cube complexes covered by products of $n$ trees and show that these cube complexes lead to new solutions of the Yang-Baxter equations.

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Alina Vdovina. 2020-07-01. Drinfeld-Manin solutions of the Yang-Baxter equation coming from cube complexes. https://arxiv.org/abs/2007.01163

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