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On Pentagon, Ten-Term, and Tetrahedron Relations

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Abstract:

It is shown that the tetrahedron equation under the substitution , where P 23 is the permutation operator, is reduced to a pair of pentagon and one ten-term equations on operators S and . 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.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique ENSLAPP, ENSLyon, 46 Allée d'Italie, 69007 Lyon, France, , , , , , FR

    R. M. Kashaev

  2. Scientific Center of Institute of Nuclear Physics SB RAS, Protvino, Moscow Region 142 284, Russia, , , , , , RO

    S. M. Sergeev

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  1. R. M. Kashaev
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  2. S. M. Sergeev
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Received: Received: 8 August 1996 / Accepted: 25 November 1997

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Kashaev, R., Sergeev, S. On Pentagon, Ten-Term, and Tetrahedron Relations . Comm Math Phys 195, 309–319 (1998). https://doi.org/10.1007/s002200050391

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  • DOI: https://doi.org/10.1007/s002200050391

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