Lifting to cluster-tilting objects in higher cluster categories

TL;DR

This paper demonstrates that tilting modules over $d$-cluster-tilted algebras can be lifted to $d$-cluster-tilting objects within the corresponding higher cluster categories, advancing the understanding of their structural relationships.

Contribution

It establishes that tilting modules over $d$-cluster-tilted algebras lift to $d$-cluster-tilting objects in higher cluster categories, revealing a new connection between algebraic and categorical structures.

Findings

Tilting modules over $d$-cluster-tilted algebras lift to $d$-cluster-tilting objects.

Provides a method to construct $d$-cluster-tilting objects from tilting modules.

Enhances understanding of the relationship between algebraic modules and categorical objects.

Abstract

In this note, we consider the $d$-cluster-tilted algebras, the endomorphism algebras of $d$-cluster-tilting objects in $d$-cluster categories. We show that a tilting module over such an algebra lifts to a $d$-cluster-tilting object in this $d$-cluster category.