相关论文: Classifying global dimensions of category algebras…
In a general triangulated category, the finiteness of the finitistic dimension serves as a prerequisite for a categorical obstruction, via the singularity category, to the existence of bounded $t$-structures. In this paper, we investigate…
EI categories can be thought of as amalgams of finite posets and finite groups and therefore the associated algebras are built up from incidence algebras and group algebras of finite groups. For this particular class of algebras we present…
In this paper, we explore when a locally finite triangulated category has dimension zero or finite representation type. We also study generation of derived categories by orthogonal subcategories.
We introduce a notion of global dimension for a triangulated category relative to a compact silting object. We prove that the finiteness of this dimension is an intrinsic property of the triangulated category itself and, therefore,…
We provide some background on the category of classifiable $\mathrm{C}^*$-algebras, whose objects are infinite-dimensional, simple, separable, unital $\mathrm{C}^*$-algebras that have finite nuclear dimension and satisfy the universal…
We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…
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…
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
We give a nontrivial lower bound for global dimension of a spherical fusion category.
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
In this article we obtain lower and upper bounds for global dimensions of a class of artinian algebras in terms of global dimensions of a finite subset of their artinian subalgebras. Finding these bounds for the global dimension of an…
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.
We classify simple representations of Khovanov-Lauda-Rouquier algebras in finite type. The classification is in terms of a standard family of representations that is shown to yield the dual PBW basis in the Grothendieck group. Finally, we…
The finitistic dimension of a triangulated category is introduced. For the category of perfect complexes over a ring it is shown that this dimension is finite if and only if the small finitistic dimension of the ring is finite.
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…
EI-categories are a simultaneous generalisation of finite groups and finite quivers without oriented cycles. It is therefore a natural question to ask for a characterisation of finite representation type. For special classes of…
We classify braided generalized near-group fusion categories whose global dimension is not an integer; there are exactly two up to Grothendieck equivalence and taking products with braided pointed fusion categories.
In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among their finitistic or global dimensions. This is closely…
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.
In this paper, we construct derived equivalences between matrix subrings. As applications, we calculate the global dimensions and the finitistic dimensions of some matrix subrings. And we show that the finitistic dimension conjecture holds…