Electric network and Hirota type 4-simplex maps

2023/03/23 by Konstantinou-Rizos, S. · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2303.13333

Abstract

Bazhanov--Stroganov (4-simplex) maps are set-theoretical solutions to the 4-simplex equation, namely the fourth member of the family of n-simplex equations, which are fundamental equations of mathematical physics. In this paper, we develop a method for constructing Bazhanov--Stroganov maps as extensions of tetrahedron maps which are set-theoretical solutions to the Zamolodchikov tetrahedron (3-simplex) equation. We employ this method to construct birarional Bazhanov--Stroganov maps which boil down to the famous electric network and Hirota tetrahedron maps at a certain limit.

Cited by

• From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations

Related

• On the solutions of the local Zamolodchikov tetrahedron equation
• Novel solutions to the tetrahedron equation
• Nonlinear Schrödinger type tetrahedron maps
• From NLS type matrix refactorisation problems to set-theoretical solutions of the 2- and 3-simplex equations
• Set-theoretical solutions of simplex equations