Cohomology of the rational “electric” tetrahedron relation

Аннотация

A tetrahedral cochain complex is generalized to the case of the functional “electric” solution of the tetrahedron equation, which is expressed in terms of rational functions. The nontrivial part of the 3-cohomology group for this solution is calculated. It turns out to be the free Abelian group with one generator; the generator is explicitly specified.