### Abstract

It is shown that the tetrahedron equation under the substitution R_{123} = S̄_{13}P_{23}S_{13}, where P_{23} is the permutation operator, is reduced to a pair of pentagon and one ten-term equations on operators S and S̄. Examples of infinite dimensional solutions are found. O-doubles of Novikov, which generalize the Heisenberg double of a Hopf algebra, provide a particular algebraic solution to the problem.

Original language | English |
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Pages (from-to) | 309-319 |

Number of pages | 11 |

Journal | Communications in Mathematical Physics |

Volume | 195 |

Issue number | 2 |

DOIs | |

Publication status | Published - 11 Jul 1998 |

Externally published | Yes |

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## Cite this

Kashaev, R. M., & Sergeev, S. M. (1998). On pentagon, ten-term, and tetrahedron relations.

*Communications in Mathematical Physics*,*195*(2), 309-319. https://doi.org/10.1007/s002200050391