On a conjecture about dominant dimensions of algebras

Abstract

For every $n\ge 1$, we present examples of algebras $A$ having dominant dimension $n$, such that the algebra $B=En{d}_A(I_0\oplus {\Omega }^{-n}(A))$ has dominant dimension different from $n$, where $I_0$ is the injective hull of $A$. This gives a counterexample to conjecture 2 of Chen and Xi. While the conjecture is false in general, we show that a large class of algebras containing higher Auslander algebras satisfies the property in the conjecture.

9 pages