Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras

• URL: http://arxiv.org/abs/2404.11501v2
• Date: Wed, 8 May 2024 04:35:36 GMT
• Title: Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras
• Authors: Pramod Padmanabhan, Vladimir Korepin,
• Abstract summary: Yang-Baxter equation, Zamalodchikov's tetrahedron equation and Bazhanov-Stroganov equation are special cases. We describe a universal method to solve these equations using Clifford algebras.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Bethe Ansatz was discoverd in 1932. Half a century later its algebraic structure was unearthed: Yang-Baxter equation was discovered, as well as its multidimensional generalizations [tetrahedron equation and $d$-simplex equations]. Here we describe a universal method to solve these equations using Clifford algebras. The Yang-Baxter equation ($d=2$), Zamalodchikov's tetrahedron equation ($d=3$) and the Bazhanov-Stroganov equation ($d=4$) are special cases. Our solutions form a linear space. This helps us to include spectral parameters. Potential applications are discussed.

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