### 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 |
---|---|

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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*Modern Physics Letters A*,

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

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*Modern Physics Letters A*, vol. 12, no. 19, pp. 1393-1410. https://doi.org/10.1142/S0217732397001424

**Two-dimensional R-matrices - Descendants of three-dimensional R-matrices.** / Sergeev, S. M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Two-dimensional R-matrices - Descendants of three-dimensional R-matrices

AU - Sergeev, S. M.

PY - 1997/6/21

Y1 - 1997/6/21

N2 - 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 Uq(A(1) r) is another projection of Σ(A(1) r).

AB - 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 Uq(A(1) r) is another projection of Σ(A(1) r).

UR - http://www.scopus.com/inward/record.url?scp=0039715697&partnerID=8YFLogxK

U2 - 10.1142/S0217732397001424

DO - 10.1142/S0217732397001424

M3 - Article

VL - 12

SP - 1393

EP - 1410

JO - Modern Physics Letters A

JF - Modern Physics Letters A

SN - 0217-7323

IS - 19

ER -