On pentagon, ten-term, and tetrahedron relations
R. M. Kashaev, S. M. Sergeev
Abstract
The tetrahedron equation in a special substitution is reduced to a pair of pentagon and one ten-term equations. Various examples of 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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