On a conjecture about Morita algebras

TL;DR

This paper presents a counterexample to a conjecture by Chen and Xi, showing that an algebra derived from a Morita algebra via a tilting module can have high dominant dimension without being Morita.

Contribution

It provides the first known counterexample to the conjecture, demonstrating a nuanced behavior of dominant dimension in relation to Morita algebras.

Findings

Counterexample to Chen and Xi's conjecture

Algebra with dominant dimension ≥ 2 not Morita

Insights into tilting modules and Morita algebras

Abstract

We give an example of a Morita algebra $A$ with a tilting module $T$ such that the algebra $End_A(T)$ has dominant dimension at least two but is not a Morita algebra. This provides a counterexample to a conjecture by Chen and Xi from \cite{CX}.