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

Autor:	Vdovina, Alina
Rok vydání:	2020
Předmět:	Mathematics - Quantum Algebra Mathematics - Combinatorics Mathematics - Group Theory 16T25 20F65
Druh dokumentu:	Working Paper
Popis:	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. Comment: 14 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1710.10306, arXiv:1304.5549
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2007.01163 Zobrazit plný text záznamu View this record from Arxiv