122 citations
- Lomonosov Moscow State UniversityRU24 papers
- Moscow Institute of Physics and TechnologyRU20 papers
- Institute for Information Transmission ProblemsRU15 papers
- Steklov Mathematical InstituteRU10 papers
- Deutsches Elektronen-Synchrotron DESYDE9 papers
- National Research Nuclear University MEPhIRU8 papers
- National Research University Higher School of EconomicsRU8 papers
- Kazan Federal UniversityRU5 papers
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15 papers · 1 filter
Matrix Lax pairs under the gauge equivalence relation induced by the gauge group action and Miura-type transformations for lattice equations
Sergei Igonin
In this paper we explore interconnections of differential-difference matrix Lax representations (Lax pairs), gauge transformations, and discrete Miura-type transformations (MTs), w…
Local Yang--Baxter correspondences and set-theoretical solutions to the Zamolodchikov tetrahedron equation
S. Igonin, S. Konstantinou-Rizos
We study tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov tetrahedron equation, and their matrix Lax representations defined by the local Yang--Baxter equ…
Birational solutions to the set-theoretical 4-simplex equation
S. Konstantinou-Rizos
The 4-simplex equation is a higher-dimensional analogue of Zamolodchikov's tetrahedron equation and the Yang--Baxter equation which are two of the most fundamental equations of mat…
Set-theoretical solutions to the Zamolodchikov tetrahedron equation on associative rings and Liouville integrability
Sergei Igonin
This paper is devoted to tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov tetrahedron equation. We construct a family of tetrahedron maps on associative r…
Noncommutative solutions to Zamolodchikov's tetrahedron equation and matrix six-factorisation problems
Sotiris Konstantinou-Rizos
It is known that the local Yang--Baxter equation is a generator of potential solutions to Zamolodchikov's tetrahedron equation. In this paper, we show under which additional condit…
Algebraic and differential-geometric constructions of set-theoretical solutions to the Zamolodchikov tetrahedron equation
Sergei Igonin, Sotiris Konstantinou-Rizos
We present several algebraic and differential-geometric constructions of tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov tetrahedron equation. In particu…