### Abstract

A local (or modified) Yang-Baxter equation (LYBE) gives a functional map from the parameters of the weights in the left-hand side to the parameters of the corresponding weights in the right-hand side of the LYBE. Such maps solve the functional tetrahedron equation. In this Letter, all the maps associated with LYBE's of the ferro-electric type with a single parameter in each weight matrix are classified.

Original language | English |
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Pages (from-to) | 113-119 |

Number of pages | 7 |

Journal | Letters in Mathematical Physics |

Volume | 45 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2 Jul 1998 |

Externally published | Yes |

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*Letters in Mathematical Physics*, vol. 45, no. 2, pp. 113-119. https://doi.org/10.1023/A:1007483621814

**Solutions of the functional tetrahedron equation connected with the local Yang-Baxter equation for the ferro-electric condition.** / Sergeev, S. M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Solutions of the functional tetrahedron equation connected with the local Yang-Baxter equation for the ferro-electric condition

AU - Sergeev, S. M.

PY - 1998/7/2

Y1 - 1998/7/2

N2 - A local (or modified) Yang-Baxter equation (LYBE) gives a functional map from the parameters of the weights in the left-hand side to the parameters of the corresponding weights in the right-hand side of the LYBE. Such maps solve the functional tetrahedron equation. In this Letter, all the maps associated with LYBE's of the ferro-electric type with a single parameter in each weight matrix are classified.

AB - A local (or modified) Yang-Baxter equation (LYBE) gives a functional map from the parameters of the weights in the left-hand side to the parameters of the corresponding weights in the right-hand side of the LYBE. Such maps solve the functional tetrahedron equation. In this Letter, all the maps associated with LYBE's of the ferro-electric type with a single parameter in each weight matrix are classified.

KW - tetrahedron equation

KW - 2 + 1 integrability

KW - local Yang-Baxter equation

UR - http://www.scopus.com/inward/record.url?scp=0000101463&partnerID=8YFLogxK

U2 - 10.1023/A:1007483621814

DO - 10.1023/A:1007483621814

M3 - Article

VL - 45

SP - 113

EP - 119

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

IS - 2

ER -