### Abstract

A large class of 3-dimensional integrable lattice spin models is constructed. The starting point is an invertible canonical mapping operator R_{1,2,3} in the space of a triple Weyl algebra. R_{1,2,3} is derived postulating a current branching principle together with a Baxter Z-invariance. The tetrahedron equation for R_{1,2,3} follows without further calculation. If the Weyl parameter is taken to be a root of unity, R_{1,2,3} decomposes into a matrix conjugation operator R _{1,2,3} and a c-number functional mapping R_{1,2,3} ^{(f)}. The operator R_{1,2,3} satisfies a modified tetrahedron equation (MTE) in which the "rapidities" are solutions of a classical integrable Hirota-type equations. R_{1,2,3} 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.

Original language | English |
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Pages (from-to) | 179-204 |

Number of pages | 26 |

Journal | International Journal of Modern Physics A |

Volume | 19 |

Issue number | SUPPL. 2 |

Publication status | Published - May 2004 |

Externally published | Yes |

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### Cite this

*International Journal of Modern Physics A*,

*19*(SUPPL. 2), 179-204.