Geodesic
Set-theoretical solutions of the~ Zamolodchikov tetrahedron equation on associative rings and Liouville integrability
Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 2, pp. 263-272

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This paper is devoted to tetrahedron maps, which are set-theoretical solutions of the Zamolodchikov tetrahedron equation. We construct a family of tetrahedron maps on associative rings. The obtained maps are new to our knowledge. We show that matrix tetrahedron maps derived previously are a particular case of our construction. This provides an algebraic explanation of the fact that the matrix maps satisfy the tetrahedron equation. Also, Liouville integrability is established for some of the constructed maps.
Keywords: Zamolodchikov tetrahedron equation, associative ring, Liouville integrability.
Mots-clés : tetrahedron map 
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     author = {S. Igonin},
     title = {Set-theoretical solutions of the~ {Zamolodchikov} tetrahedron equation on associative rings and {Liouville} integrability},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {263--272},
     publisher = {mathdoc},
     volume = {212},
     number = {2},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_212_2_a6/}
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S. Igonin. Set-theoretical solutions of the~ Zamolodchikov tetrahedron equation on associative rings and Liouville integrability. Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 2, pp. 263-272. http://geodesic.mathdoc.fr/item/TMF_2022_212_2_a6/