### Abstract

Original language | English |
---|---|

Pages (from-to) | 179-204 |

Number of pages | 26 |

Journal | International Journal of Modern Physics A |

Volume | A19S2 |

Publication status | Published - 2004 |

Externally published | Yes |

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### Cite this

*International Journal of Modern Physics A*,

*A19S2*, 179-204.

}

*International Journal of Modern Physics A*, vol. A19S2, pp. 179-204.

**The modified tetrahedron equation amd its solutions.** / Von Gehlen, Gunter; Pakuliak, Stanislav; Sergeev, Sergey.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The modified tetrahedron equation amd its solutions

AU - Von Gehlen, Gunter

AU - Pakuliak, Stanislav

AU - Sergeev, Sergey

PY - 2004

Y1 - 2004

N2 - A large class of 3-dimensional integrable lattice spin models is constructed. The starting point is an invertible canonical mapping operator R1,2,3 in the space of a triple Weyl algebra. R1,2,3 is derived postulating a current branching principle together with a Baxter Z-invariance. The tetrahedron equation for R1,2,3 follows without further calculation. If the Weyl parameter is taken to be a root of unity, R1,2,3 decomposes into a matrix conjugation operator R 1,2,3 and a c-number functional mapping R1,2,3(f). The operator R1,2,3 satisfies a modified tetrahedron equation (MTE) in which the "rapidities" are solutions of a classical integrable Hirota-type equations. R1,2,3 can be represented in terms of the Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of Gauss functions. The paper summarizes several recent publications on the subject

AB - A large class of 3-dimensional integrable lattice spin models is constructed. The starting point is an invertible canonical mapping operator R1,2,3 in the space of a triple Weyl algebra. R1,2,3 is derived postulating a current branching principle together with a Baxter Z-invariance. The tetrahedron equation for R1,2,3 follows without further calculation. If the Weyl parameter is taken to be a root of unity, R1,2,3 decomposes into a matrix conjugation operator R 1,2,3 and a c-number functional mapping R1,2,3(f). The operator R1,2,3 satisfies a modified tetrahedron equation (MTE) in which the "rapidities" are solutions of a classical integrable Hirota-type equations. R1,2,3 can be represented in terms of the Bazhanov-Baxter Fermat curve cyclic functions, or alternatively in terms of Gauss functions. The paper summarizes several recent publications on the subject

M3 - Article

VL - A19S2

SP - 179

EP - 204

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

SN - 0217-751X

ER -