On one-point extensions of cluster-tilted algebras

TL;DR

This paper introduces a new operation for cluster-tilted algebras that involves adding a vertex and arrows, expanding the class of such algebras through one-point extensions.

Contribution

It defines a novel operation linking modules in local slices to new cluster-tilted algebras via one-point extensions.

Findings

Operation preserves cluster-tilted structure

Adds a vertex and arrows to the quiver

Provides a method to construct new cluster-tilted algebras

Abstract

We define an operation which associates to a pair (B,M) where B is a cluster-tilted algebra and M is a B-module which lies in a local slice of B, a new cluster-tilted algebra B'. In terms of the quivers, this operation corresponds to adding one vertex (and arrows).