3 papers
math.QA2025
Heptagon relations from a simplicial 3-cocycle, and their cohomology
Igor G. Korepanov
We introduce new algebraic structures associated with heptagon relations -- higher analogue of the well-known pentagon. The main points we deal with are: (i) polygon relations as a…
math.QA2025
Self-similarity on 4d cubic lattice
Igor G. Korepanov
A phenomenon of "algebraic self-similarity" on 3d cubic lattice, providing what can be called an algebraic analogue of Kadanoff--Wilson theory, is shown to possess a 4d version as…
math.QA2024
Solutions to quantum tetrahedron equation with two colors and nonnegative matrix entries
Igor G. Korepanov
In this short note, we construct solutions to quantum tetrahedron equation of the kind "with variables on the edges". Each of these variables takes just two values, called sometime…