From tilted to cluster-tilted algebras of Dynkin type

TL;DR

This paper explores the relationship between cluster-tilted algebras and tilted algebras of Dynkin type, providing insights into their structural connections in the context of finite representation type.

Contribution

It establishes a connection between cluster-tilted and tilted algebras of Dynkin type over algebraically closed fields, enhancing understanding of their structural relationship.

Findings

Cluster-tilted algebras of finite type relate to tilted algebras.

Structural correspondence between the two algebra types is clarified.

Results apply to algebras over algebraically closed fields.

Abstract

We show how a cluster-tilted algebra of finite representation type is related to the corresponding tilted algebra, in the case of algebras defined over an algebraically closed field.