Two-color solutions of set-theoretic tetrahedron equation and their cohomologies

2015/04/10 by Nurlan M. Sadykov, Sadykov, Nurlan M.
Mathematics · #Point processes and geometric inequalities #Random Matrices and Applications #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1504.03314

Abstract

All solutions of the set-theoretic constant tetrahedron equation with two colors are found, and some of their properties are analyzed. The list includes 406 solutions - we call them R-operators, - most of which are degenerate (non-bijective). Then, we calculate the 3-cohomologies for our R-operators, and discuss the applicability of our results to 3-dimensional statistical physics.

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