Deformed mesh algebras of Dynkin type $\mathbb{F}_4$

TL;DR

This paper proves that all deformed mesh algebras of type F4 are structurally identical to the canonical mesh algebra of the same type, establishing their isomorphism.

Contribution

It demonstrates that any deformation of the mesh algebra of type F4 is essentially equivalent to the canonical form, simplifying classification.

Findings

All deformed mesh algebras of type F4 are isomorphic to the canonical mesh algebra.

The result unifies the understanding of deformed and canonical mesh algebras of this type.

The proof confirms the rigidity of the algebraic structure for type F4.

Abstract

We prove that every deformed mesh algebra of type $\mathbb{F}_4$ is isomorphic to the canonical mesh algebra of type $\mathbb{F}_4$.