Abstract
The tetrahedron equation arises as a generalization of the famous Yang-Baxter equation to the2+1-dimensional quantum field theory and three-dimensional statistical mechanics. Not much is known about its solutions. In the present paper, a systematic method of constructing nontrivial solutions to the tetrahedron equation with spin-like variables on the links is described. The essence of this method is the use of the so-called tetrahedral Zamolodchikov algebras. Bibliography:12 titles.
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