Tetrahedron equation

introduction

• The tetrahedron equation arises as a generalization of the Yang--Baxter equation to the 2+1-dimensional quantum field theory and the 3-dimensional statistical mechanics
• tetrahedral Zamolodchikov algebras

related items

• Yang-Baxter equation (YBE)
• R-matrix
• Simple exclusion process

expositions

• Kuniba, Atsuo. “Combinatorial Yang-Baxter Maps Arising from Tetrahedron Equation.” arXiv:1509.02245 [math-Ph, Physics:nlin], September 7, 2015. http://arxiv.org/abs/1509.02245.
• Kuniba, Atsuo, and Masato Okado. ‘Tetrahedron Equation and Quantum $R$ Matrices for $q$-Oscillator Representations’. arXiv:1411.2213 [math-Ph, Physics:nlin], 9 November 2014. http://arxiv.org/abs/1411.2213.

articles

• Kuniba, Atsuo, Shouya Maruyama, and Masato Okado. “Multispecies Totally Asymmetric Zero Range Process: II. Hat Relation and Tetrahedron Equation.” arXiv:1602.04574 [math-Ph, Physics:nlin], February 15, 2016. http://arxiv.org/abs/1602.04574.
• Korepanov, I. G. “Three-Dimensionalizing the Eight-Vertex Model.” arXiv:1601.00794 [math-Ph], January 5, 2016. http://arxiv.org/abs/1601.00794.
• Kuniba, Atsuo, Shouya Maruyama, and Masato Okado. “Multispecies TASEP and the Tetrahedron Equation.” arXiv:1509.09018 [math-Ph, Physics:nlin], September 30, 2015. http://arxiv.org/abs/1509.09018.
• Talalaev, Dmitry V. ‘Zamolodchikov Tetrahedral Equation and Higher Hamiltonians of 2d Quantum Integrable Systems’. arXiv:1505.06579 [hep-Th, Physics:math-Ph], 25 May 2015. http://arxiv.org/abs/1505.06579.
• Sadykov, Nurlan M. ‘Two-Color Solutions of Set-Theoretic Tetrahedron Equation and Their Cohomologies’. arXiv:1504.03314 [math-Ph], 10 April 2015. http://arxiv.org/abs/1504.03314.
• Kuniba, Atsuo, Masato Okado, and Sergey Sergeev. ‘Tetrahedron Equation and Generalized Quantum Groups’. arXiv:1503.08536 [math-Ph, Physics:nlin], 30 March 2015. http://arxiv.org/abs/1503.08536.
• Kuniba, Atsuo, and Shouya Maruyama. “A Polynomial Formula for the Solution of 3D Reflection Equation.” arXiv:1411.7763 [math-Ph, Physics:nlin], November 28, 2014. http://arxiv.org/abs/1411.7763.
• Kuniba, Atsuo, Masato Okado, and Sergey Sergeev. “Tetrahedron Equation and Quantum $R$ Matrices for Modular Double of $U_q(D^{(2)}_{n+1}), U_q(A^{(2)}_{2n})$ and $U_q(C^{(1)}_{n})$.” arXiv:1409.1986 [math-Ph, Physics:nlin], September 6, 2014. http://arxiv.org/abs/1409.1986.
• Bytsko, Andrei, and Alexander Volkov. 2014. “Tetrahedron Equation, Weyl Group, and Quantum Dilogarithm.” arXiv:1407.5658 [math-Ph], July. http://arxiv.org/abs/1407.5658.
• Kuniba, Atsuo, and Masato Okado. “Tetrahedron Equation and Quantum R Matrices for $q$-Oscillator Representations of $U_q(A^{(2)}_{2n}), U_q(C^{(1)}_{n})$ and $U_q(D^{(2)}_{n+1})$.” arXiv:1311.4258 [math-Ph, Physics:nlin], November 17, 2013. http://arxiv.org/abs/1311.4258.
• Korepanov, I. G. “Tetrahedron Equation and the Algebraic Geometry.” arXiv:hep-th/9401076, January 17, 1994. http://arxiv.org/abs/hep-th/9401076.