Upper Bounds for Mutations of Potentials

TL;DR

This paper introduces an algebraic proof for the Laurent phenomenon in mutations of potentials, utilizing upper bounds analogous to those in cluster algebra theory, advancing understanding of algebraic structures in this context.

Contribution

It provides a new algebraic proof of the Laurent phenomenon for mutations of potentials, incorporating upper bounds into the theory.

Findings

Established algebraic proof of the Laurent phenomenon

Introduced upper bounds for mutations of potentials

Extended cluster algebra concepts to potentials

Abstract

In this note we provide a new, algebraic proof of the excessive Laurent phenomenon for mutations of potentials (in the sense of [Galkin S., Usnich A., Preprint IPMU 10-0100, 2010]) by introducing to this theory the analogue of the upper bounds from [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005), 1-52].