15 citations · 93 across the 16 of their papers we have counts for
16 papers
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…
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…
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…
Tetrahedron maps, Yang-Baxter maps, and partial linearisations
S. Igonin, V. Kolesov, S. Konstantinou-Rizos +1
We study tetrahedron maps, which are set-theoretical solutions to the Zamolodchikov tetrahedron equation, and Yang-Baxter maps, which are set-theoretical solutions to the quantum Y…
Yang--Baxter maps, Darboux transformations, and linear approximations of refactorisation problems
V. M. Buchstaber, S. Igonin, S. Konstantinou-Rizos +1
Yang--Baxter maps (YB maps) are set-theoretical solutions to the quantum Yang--Baxter equation. For a set , where is a vector space and is regarded as a space…
On Lie algebras responsible for integrability of (1+1)-dimensional scalar evolution PDEs
Sergei Igonin, Gianni Manno
Zero-curvature representations (ZCRs) are one of the main tools in the theory of integrable PDEs. In particular, Lax pairs for (1+1)-dimensional PDEs can be interpreted as ZCRs. In…