2020/07/01 by Alina Vdovina, Vdovina, Alina
Mathematics · #16T25 #20F65 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.2007.01163
openalex publication_date 2020/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The most common geometric interpretation of the Yang-Baxter equation is by\nbraids, knots and relevant Reidemeister moves. So far, cubes were used for\nconnections with the third Reidemeister move only. We will show that there are\nhigher-dimensional cube complexes solving the D-state Yang-Baxter equation\nfor arbitrarily large D. More precisely, we introduce explicit constructions\nof cube complexes covered by products of n trees and show that these cube\ncomplexes lead to new solutions of the Yang-Baxter equations.\n