Related papers: Dominant dimension and tilting modules
In this paper, we aim to obtain some results under the condition that the dual of a module over a commutative Noetherian ring has finite Gorenstein dimension. In this direction, we derive results involving vanishing of Ext as well as the…
Let $R$ be a left noetherian ring, $S$ a right noetherian ring and $_RU$ a generalized tilting module with $S={\rm End}(_RU)$. The injective dimensions of $_RU$ and $U_S$ are identical provided both of them are finite. Under the assumption…
Let $\mathbb{Z}$ be the integer numbers, $\mathbb{K}$ an algebraically closed field, $\Lambda$ a finite dimensional $\mathbb{K}$-algebra, mod$\Lambda$ the category of finitely generated right modules, proj$\Lambda$ the full subcategory of…
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 $n$.…
We develop silting theory of a noetherian algebra $\Lambda$ over a commutative noetherian ring $R$. We study mutation theory of $2$-term silting complexes of $\Lambda$, and as a consequence, we see that mutation exists. As in the case of…
We study homological behavior of modules satisfying the Auslander condition. Assume that $\mathcal{AC}$ is the class of left $R$-modules satisfying the Auslander condition. It is proved that each cycle of an exact complex with each term in…
We revisit faithfully balanced modules. These are faithful modules having the double centralizer property. For finite-dimensional algebras our main tool is the category ${\rm cogen}^1(M)$ of modules with a copresentation by summands of…
In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length…
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…
Let $\mathbb{Z}$ be the integer numbers, $\mathbb{k}$ an algebraically closed field, $\Lambda$ a finite dimensional $\mathbb{k}$-algebra, mod$\Lambda$ the category of finitely generated right modules, proj$\Lambda$ the full subcategory of…
We study finiteness conditions on large tilting modules over arbitrary rings. We then turn to a hereditary artin algebra R and apply our results to the (infinite dimensional) tilting module L that generates all modules without preprojective…
Let $G=SL(2,5)$ be the special linear group of $2 \times 2$-matrices with coefficients in the field with $5$ elements. We show that the principal block over a splitting field $K$ of characteristic two of the group algebra $KG$ has a…
We provide a classification of generalized tilting modules and full exceptional sequences for the dual extension algebra of the path algebra of a uniformly oriented linear quiver modulo the ideal generated by paths of length two with its…
In this paper, we prove a higher dimensional version of Auslander-Iyama-Solberg correspondence. Iyama and Solberg have shown a bijection between $n$-minimal Auslander-Gorenstein algebras and $n$-precluster tilting modules. If $A$ is an…
We say that an algebra $\Lambda$ over a commutative noetherian ring $R$ is Calabi-Yau of dimension $d$ ($d$-CY) if the shift functor $[d]$ gives a Serre functor on the bounded derived category of the finite length $\Lambda$-modules. We show…
The blob algebra is a finite-dimensional quotient of the Hecke algebra of type $B$ which is almost always quasi-hereditary. We construct the indecomposable tilting modules for the blob algebra over a field of characteristic $0$ in the…
Let T be a tilting object in a triangulated category equivalent to the bounded derived category of a hereditary abelian category with finite dimensional homomorphism spaces and split idempotents. This text investigates the strong global…
We give a complete description of finite dimensional selfinjective algebras over an algebraically closed field whose Auslander-Reiten quiver admits a generalized standard family of quasi-tubes maximally saturated by simple and projective…
Happel and Unger reconstructed hereditary algebras from their posets of tilting modules. Inspired by this result, we try removing the assumption to be hereditary. However, it would be unfortunately fail in general: e.g. every selfinjective…
We consider the question of whether the injective modules generate the unbounded derived category of a ring as a triangulated category with arbitrary coproducts. We give an example of a non-Noetherian commutative ring where they don't, but…