Dimension two twisted graded Calabi--Yau algebras on two-vertex quivers

TL;DR

This paper classifies dimension two twisted graded Calabi--Yau algebras on two-vertex quivers and explores isomorphism problems for related algebras on larger quivers, advancing understanding of their structure.

Contribution

It provides a classification of these algebras up to isomorphism and addresses the isomorphism problem for broader classes of such algebras.

Findings

Complete classification of dimension two twisted graded Calabi--Yau algebras on two-vertex quivers.

Analysis of isomorphism problems for families of these algebras on larger quivers.

Identification of conditions under which these algebras are isomorphic.

Abstract

We classify, up to isomorphism, twisted graded Calabi--Yau algebras of dimension two on two-vertex quivers. By work of Reyes and Rogalski, such algebras may be presented as quotients of translation quivers by mesh relations. We also consider the isomorphism problem for certain families of twisted graded Calabi--Yau algebras on larger quivers.