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

Lookup NU author(s): Dr Alina Vdovina

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Abstract

© 2021 World Scientific Publishing Company.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.

Publication metadata

Author(s): Vdovina A

Publication type: Article

Publication status: Published

Journal: International Journal of Algebra and Computation

Year: 2021

Volume: 31

Issue: 4

Pages: 775-788

Print publication date: 01/06/2021

Online publication date: 31/05/2021

Acceptance date: 08/03/2021

ISSN (print): 0218-1967

ISSN (electronic): 1793-6500

Publisher: World Scientific

URL: https://doi.org/10.1142/S0218196721500351

DOI: 10.1142/S0218196721500351

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