### Abstract

Finite layers of three-dimensional models can be regarded as two-dimensional with complicated multi-stated weights. The tetrahedron equation in 3D provides the Yang-Baxter equation for this composite weights in 2D. Such solutions of the Yang-Baxter equation are constructed for the simplest operator solution of the tetrahedron equation. These R-matrices can be regarded as a special projection of universal R-matrix for some Drinfeld double Σ(A^{(1)}
_{r}), associated with the affine algebra A^{(1)}
_{r}. Usual R-matrix for U_{q}(A^{(1)}
_{r}) is another projection of Σ(A^{(1)}
_{r}).

Original language | English |
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Pages (from-to) | 1393-1410 |

Number of pages | 18 |

Journal | Modern Physics Letters A |

Volume | 12 |

Issue number | 19 |

DOIs | |

Publication status | Published - 21 Jun 1997 |

Externally published | Yes |

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## Cite this

Sergeev, S. M. (1997). Two-dimensional R-matrices - Descendants of three-dimensional R-matrices.

*Modern Physics Letters A*,*12*(19), 1393-1410. https://doi.org/10.1142/S0217732397001424