Related papers: Upper bounds for dominant dimensions of gendo-symm…

The Nakayama conjecture states that an algebra of infinite dominant dimension should be self-injective. Motivated by understanding this conjecture in the context of derived categories, we study dominant dimensions of algebras under derived…

Optimal upper bounds are provided for the dominant dimensions of Nakayama algebras and more generally algebras $A$ with an idempotent $e$ such that there is a minimal faithful injective-projective module $eA$ and such that $eAe$ is a…

We show that a finite dimensional algebra $A$ has dominant dimension at least $n \geq 2$ if and only if the regular bimodule $A$ is $n$-torsionfree if and only if $A \cong \Omega^{n}(\text{Tr}(\Omega^{n-2}(V)))$ as $A$-bimodules, where…

We show that a faithful projective-injective module over a finite-dimensional algebra $A$ has the double centraliser property if and only if $A$ as a bimodule is reflexive. More generally, we provide a new characterisation of the classical…

We generalise a theorem of Tachikawa about reflexive Auslander-Reiten sequences. We apply this to give a new characterisation of the dominant dimension of gendo-symmetric algebras. We also generalise a formula due to Reiten about the…

Motivated by understanding the Nakayama conjecture which states that algebras of infinite dominant dimension should be self-injective, we study self-orthogonal modules with virtually Gorenstein endomorphism algebras and prove the following…

We give new improved bounds for the dominant dimension of Nakayama algebras and use those bounds to give a classification of Nakayama algebras with $n$ simple modules that are higher Auslander algebras with global dimension at least $n$.…

For every $n \geq 1$, we present examples of algebras $A$ having dominant dimension $n$, such that the algebra $B=End_A(I_0 \oplus \Omega^{-n}(A))$ has dominant dimension different from $n$, where $I_0$ is the injective hull of $A$. This…

Recently, Chen and Koenig in \cite{CheKoe} and Iyama and Solberg in \cite{IyaSol} independently introduced and characterised algebras with dominant dimension coinciding with the Gorenstein dimension and both dimensions being larger than or…

We prove that a finite dimensional algebra $A$ with representation-finite subcategory consisting of modules that are semi-Gorenstein-projective and $n$-th syzygy modules is left weakly Gorenstein. This generalises a theorem of Ringel and…

We prove that the finitistic dimension conjecture, the Gorenstein Symmetry Conjecture, the Wakamatsu-tilting conjecture and the generalized Nakayama conjecture hold for artin algebras which can be realized as endomorphism algebras of…

Let $A$ be a Nakayama algebra with $n$ simple modules and a simple module $S$ of even projective dimension $m$. Choose $m$ minimal such that a simple $A$-module with projective dimension $2m$ exists, then we show that the global dimension…

Tachikawa's second conjecture predicts that a finitely generated, orthogonal module over a finite-dimensional self-injective algebra is projective. This conjecture is an important part of the Nakayama conjecture. Our principal motivation of…

We study which algebras have tilting modules that are both generated and cogenerated by projective-injective modules. Crawley-Boevey and Sauter have shown that Auslander algebras have such tilting modules; and for algebras of global…

For Nakayama algebras $A$, we prove that in case $Ext_A^1(M,M) \neq 0$ for an indecomposable $A$-module $M$, we have that the projective dimension of $M$ is infinite. As an application we give a new proof of a classical result from…

We study certain special tilting and cotilting modules for an algebra with positive dominant dimension, each of which is generated or cogenerated (and usually both) by projective-injectives. These modules have various interesting…

The aim of this paper is to study the dominant dimension of two important classes of finite dimensional algebras, namely, hereditary algebras and tree algebras. We derive an explicit formula for the dominant dimension of each class.

Derived equivalences between finite dimensional algebras do, in general, not pass to centraliser (or other) subalgebras, nor do they preserve homological invariants of the algebras, such as global or dominant dimension. We show that,…

We show that the Calabi-Yau dimension of the stable module category of a selfinjective algebra of finite representation type is determined by the action of the Nakayama and suspension functors on objects. Our arguments are based on recent…

Given an algebra with an idempotent, we introduce two procedures to construct families of new algebras, termed mirror-reflective algebras and reduced mirror-reflective algebras. We then establish connections among these algebras by…