### 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

*Communications in Mathematical Physics*,

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

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*Communications in Mathematical Physics*, vol. 195, no. 2, pp. 309-319. https://doi.org/10.1007/s002200050391

**On pentagon, ten-term, and tetrahedron relations.** / Kashaev, R. M.; Sergeev, S. M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On pentagon, ten-term, and tetrahedron relations

AU - Kashaev, R. M.

AU - Sergeev, S. M.

PY - 1998/7/11

Y1 - 1998/7/11

N2 - It is shown that the tetrahedron equation under the substitution R123 = S̄13P23S13, where P23 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.

AB - It is shown that the tetrahedron equation under the substitution R123 = S̄13P23S13, where P23 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.

KW - tetrahedron equation

UR - http://www.scopus.com/inward/record.url?scp=0001461396&partnerID=8YFLogxK

U2 - 10.1007/s002200050391

DO - 10.1007/s002200050391

M3 - Article

VL - 195

SP - 309

EP - 319

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 2

ER -