Laurent phenomenon algebras and the discrete BKP equation

TL;DR

This paper constructs Laurent phenomenon algebras whose cluster variables satisfy the discrete BKP equation and its reductions, linking algebraic structures to integrable difference equations.

Contribution

It introduces a new class of Laurent phenomenon algebras with generalized mutation-period property that encode solutions to the discrete BKP equation and its reductions.

Findings

Laurent phenomenon algebras satisfy the discrete BKP equation

Reductions of seeds correspond to reductions of difference equations

Generalized mutation-period property enables algebraic encoding of integrable systems

Abstract

We construct the Laurent phenomenon algebras the cluster variables of which satisfy the discrete BKP equation and other difference equations obtained by its reduction. These Laurent phenomenon algebras are constructed from seeds with a generalization of mutation-period property. We show that a reduction of a seed corresponds to a reduction of a difference equation.