Set-theoretical solutions to the pentagon equation: a survey

Abstract

This survey aims to collect the main results of the theory of the set-theoretical solutions to the pentagon equation obtained up to now in the literature. In particular, we present some classes of solutions and raise some questions.

References in corpus (8)

• Simplex and Polygon Equations
• The Hopf modules category and the Hopf equation
• Set-theoretic solutions of the Pentagon Equation
• Heisenberg duoble, pentagon equation, structure and classification of finite dimensional Hopf algebras
• Matrix factorizations and pentagon maps
• Idempotent set-theoretical solutions of the pentagon equation
• Set-theoretical solutions of the pentagon equation on Clifford semigroups
• On the Structure of Set-Theoretic Polygon Equations