Stephen Zito

activity

20182021

collaborators

8 papers

math.RT2021

Three Results Concerning Auslander Algebras

Stephen Zito

Our first result provides a new characterization of Auslander algebras using a property of hereditary torsion pairs. The second result shows an Auslander algebra $Λ$ is left or rig…

math.RT2020

Several Results Concerning Convex Subcategories

Stephen Zito

We apply the notion of a full convex subcategory to a wide range of algebras including tilted, quasi-tilted, shod, weakly shod, left and right glued, laura, simply connected, stron…

math.RT2020

$τ$ -Tilting Finite Algebras With Nonempty Left Or Right Parts Are Representation-Finite

Stephen Zito

Let $Λ$ be a finite dimensional algebra such that $L_{Λ}$ or $R_{Λ} \neq = \emptyset$ . Then $Λ$ is $τ$ -tilting finite if and only if $Λ$ is representation-finite.

math.RT2020

1-Auslander-Gorenstein algebras which are tilted

Stephen Zito

Let $Λ$ be a 1-Auslander-Gorenstein Algebra. We give a necessary and sufficient condition for $Λ$ to be a tilted algebra.

math.RT2019

$τ$ -Tilting Finite Cluster-Tilted Algebras

Stephen Zito

Let B be a cluster-tilted algebra. We prove that B is $τ$ -tilting finite if and only if B is representation-finite.

math.RT2018

A New Proof Concerning Quasi-Tilted Algebras

Stephen Zito

Let $Λ$ be a quasi-tilted algebra. If $Λ$ is representation-finite, it was shown by Happel, Reiten, and Smalø that $Λ$ is tilted. We provide a new, short proof of this result.

Three Results Concerning Auslander Algebras

Several Results Concerning Convex Subcategories

τ-Tilting Finite Algebras With Nonempty Left Or Right Parts Are Representation-Finite

1-Auslander-Gorenstein algebras which are tilted

τ-Tilting Finite Cluster-Tilted Algebras

A New Proof Concerning Quasi-Tilted Algebras

$τ$ -Tilting Finite Algebras With Nonempty Left Or Right Parts Are Representation-Finite

$τ$ -Tilting Finite Cluster-Tilted Algebras