Geodesic
Cohomology of the rational ``electric'' tetrahedron relation
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 2, pp. 57-71.

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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.
Mots-clés : tetrahedron equation, electric solution
Keywords: cohomology of tetrahedron relation. 
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N. M. Sadykov. Cohomology of the rational ``electric'' tetrahedron relation. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 2, pp. 57-71. http://geodesic.mathdoc.fr/item/FAA_2017_51_2_a5/

[1] F. L. Bottesi, G. R. Zemba, Critical theory of two-dimensional Mott transition: integrability and Hilbert space mapping, arXiv: 1504.05772

[2] J. Hietarinta, “Permutation-type solutions to the Yang-Baxter and other $n$-simplex equations”, J. Phys. A, 30:13 (1997), 4757 | DOI | MR | Zbl

[3] R. M. Kashaev, I. G. Korepanov, S. M. Sergeev, “Funktsionalnoe uravnenie tetraedrov”, TMF, 117:3 (1998), 370–384 | DOI | MR | Zbl

[4] I. G. Korepanov, Novye resheniya uravneniya tetraedrov, Deponirovano v VINITI No1751-V89 , Chelyabinskii politekhnicheskii institut, Chelyabinsk, 1989 http://www.researchgate.net/publication/274353173

[5] I. G. Korepanov, “A dynamical system connected with inhomogeneous 6-vertex model”, Zap. nauch. sem. POMI, 215 (1994), 178–196 ; arXiv: hep-th/9402043 | MR

[6] I. G. Korepanov, “Tetrahedral Zamolodchikov algebras corresponding to Baxter's $L$-operators”, Comm. Math. Phys., 154 (1993), 85–97 | DOI | MR | Zbl

[7] I. G. Korepanov, G. I. Sharygin, D. V. Talalaev, “Cohomologies of $n$-simplex relations”, Math. Proc. Cambridge Philos. Soc., 161:2 (2016), 203–222 ; arXiv: 1409.3127 | DOI | MR | Zbl

[8] N. Metropolis, G.-C. Rota, “Combinatorial structure of the faces of the $n$-cube”, SIAM J. Appl. Math., 35:4 (1978), 689–694 | DOI | MR | Zbl

[9] A. B. Zamolodchikov, “Tetrahedron equations and the relativistic $S$-matrix of straight-strings in $2+1$-dimensions”, Comm. Math. Phys., 79:4 (1981), 489–505 | DOI | MR