ON PENTAGON, 10-TERM, AND TETRAHEDRON RELATIONS

It is shown that the tetrahedron equation under the substitution R-123 = (S) over bar(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 operat ors S and (S) over bar. Examples of infinite dimensional solutions are found, O-doubles of Novikov, which generalize the Heisenberg double o f a Hopf algebra, provide a particular algebraic solution to the probl em.