Related papers: Dimensions of triangulated categories via Koszul o…
We give a description of the connected graded algebras which are finitely generated and presented of global dimension 2 or 3 and which are Gorenstein. These algebras are constructed from multilinear forms. We generalize the construction by…
We investigate the triangulated hull of the orbit categories of the perfect derived category and the bounded derived category of a ring concerning the power of the suspension functor. It turns out that the triangulated hull will correspond…
In this paper, we study metric completions of triangulated categories in a representation-theoretic context. We provide a concrete description of completions of bounded derived categories of hereditary finite dimensional algebras of finite…
There is a well-known class of algebras called Igusa-Todorov algebras which were introduced in relation to finitistic dimension conjecture. As a generalization of Igusa-Todorov algebras, the new notion of $(m,n)$-Igusa-Todorov algebras…
We give an upper bound for the dimension of the bounded derived categories of $(m,n)$-Igusa-Todorov algebras which is a generalization of $n$-Igusa-Todorov algebras, where $m,n$ are two nonnegative integers. As an applications, we get a new…
Let \(\Lambda\) be a finite-dimensional Koszul algebra with Koszul dual \(\Lambda^!\). We establish derived Koszul dualities at the level of bounded derived categories, both in the graded setting \(\mathsf{D}^{b}(\Lambda\textup{-gmod})\)…
We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted…
Let $\Lambda$ be an artin algebra. We give an upper bound for the dimension of the bounded derived category of the category $\mod \Lambda$ of finitely generated right $\Lambda$-modules in terms of the projective and injective dimensions of…
The class of $N$-Koszul graded algebras of finite global dimension has gained lots of attention in recent years, especially in the study of Artin-Schelter regular algebras. While structurally rich and concrete, the only known examples of…
We use the theory of approximable triangulated categories to give a condition for a proper DG-category to be reflexive in the sense of Kuznetsov and Shinder. To do this we provide another description of the completion of an approximable…
We introduce the notion of composition series of triangulated categories, which generalizes full exceptional sequences. The lengths of composition series yield invariants for triangulated categories. We study composition series of derived…
Koszul duality and covering theory are combined to realise the bounded derived category D of an algebra with radical square zero as a certain orbit category of the bounded derived category of finitely presented representations of an…
An extension of algebras is a homomorphism of algebras preserving identities. We use extensions of algebras to study the finitistic dimension conjecture over Artin algebras. Let $f: B \to A$ be an extension of Artin algebras. We denote by…
We are concerned with relating derived categories of all modules of two dual Koszul algebras defined by a locally bounded quiver. We first generalize the well known Acyclic Assembly Lemma and formalize an old method of extending a functor…
For the module category of an Artin algebra, we generalize the notion of torsion pairs to ideal torsion pairs. Instead of full subcategories of modules, ideals of morphisms of the ambient category are considered. We characterize the…
For central simple finitely generated algebras of finite Gelfand-Kirillov dimension and for their division algebras upper bounds are obtained for the transcendence degree of their commutative subalgebras and subfields respectively. In the…
The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When…
The global dimension of a triangulated category is defined to be the infimum value of the global dimensions of stability conditions on the triangulated category. In this paper, we study the global dimension of the derived category of an…
In this paper, let $(\mathcal{A},\mathcal{B},\mathcal{C})$ be a recollement of extriangulated categories. We introduce the global dimension and extension dimension of extriangulated categories, and give some upper bounds of global…
In this note we discuss three notions of dimension for triangulated categories: Rouquier dimension, diagonal dimension and Serre dimension. We prove some basic properties of these dimensions, compare them and discuss open problems.