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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 212, Number 2, Pages 263–272
DOI: https://doi.org/10.4213/tmf10275 (Mi tmf10275) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Set-theoretical solutions of the Zamolodchikov tetrahedron equation on associative rings and Liouville integrability

S. Igonin

Center of Integrable Systems, Demidov Yaroslavl State University, Yaroslavl, Russia
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DOI: https://doi.org/10.4213/tmf10275
Abstract: 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, tetrahedron map, associative ring, Liouville integrability.
Funding agency Grant number
Russian Science Foundation 21-71-30011
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-886
The work on Sections 1 and 2 was supported by the Russian Science Foundation grant No. 21-71-30011. The work on Section 3 was carried out within the framework of a development program for the Regional Scientific and Educational Mathematical Center of the Demidov Yaroslavl State University with financial support from the Ministry of Science and Higher Education of the Russian Federation (Agreement on provision of subsidy from the federal budget No. 075-02-2022-886).
Received: 27.02.2022
Revised: 27.02.2022
English version:
Theoretical and Mathematical Physics, 2022, Volume 212, Issue 2, Pages 1116–1124
DOI: https://doi.org/10.1134/S0040577922080074
Bibliographic databases:
Document Type: Article
MSC: 16T25, 81R12
Language: Russian
Citation: S. Igonin, “Set-theoretical solutions of the Zamolodchikov tetrahedron equation on associative rings and Liouville integrability”, TMF, 212:2 (2022), 263–272; Theoret. and Math. Phys., 212:2 (2022), 1116–1124
Citation in format AMSBIB
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\by S.~Igonin
\paper Set-theoretical solutions of the~ Zamolodchikov tetrahedron equation on associative rings and Liouville integrability
\jour TMF
\yr 2022
\vol 212
\issue 2
\pages 263--272
\mathnet{http://mi.mathnet.ru/tmf10275}
\crossref{https://doi.org/10.4213/tmf10275}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461556}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2022TMP...212.1116I}
\transl
\jour Theoret. and Math. Phys.
\yr 2022
\vol 212
\issue 2
\pages 1116--1124
\crossref{https://doi.org/10.1134/S0040577922080074}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85136644450}
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  • https://www.mathnet.ru/eng/tmf/v212/i2/p263
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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