相关论文: Delooping Level of Nakayama algebras

We introduce higher dimensional analogues of the Nakayama algebras from the viewpoint of Iyama's higher Auslander--Reiten theory. More precisely, for each Nakayama algebra $A$ and each positive integer $d$, we construct a finite dimensional…

Based on the fact that every finite-dimensional algebra over a field is isomorphic to the centralizer of \textbf{two} matrices, we approach the representation theory of finite-dimensional algebras over fields by centralizers of matrices.…

For any ring we propose the construction of a cover which increases the finitistic dimension on one side and decreases the finitistic dimension to zero on the opposite side. This complements recent work of Cummings.

In this paper we develop new reduction techniques for testing the finiteness of the finitistic dimension of a finite dimensional algebra over a field. Viewing the latter algebra as a quotient of a path algebra, we propose two operations on…

This is an overview article on finite-dimensional algebras and quivers, written for the Encyclopedia of Mathematical Physics. We cover path algebras, Ringel-Hall algebras and the quiver varieties of Lusztig and Nakajima.

Intuitively, the filter dimension of an algebra or a module measures how `close' standard filtrations of the algebra or the module are. In particular, for a simple algebra it also measures the growth of how `fast' one can prove that the…

Recently, Ringel introduced the resolution quiver for a connected Nakayama algebra. It is known that each connected component of the resolution quiver has a unique cycle. We prove that all cycles in the resolution quiver are of the same…

We call a finite dimensional algebra A S-connected if the projective dimensions of the simple A-modules form an interval. We prove that a Nakayama algebra A is S-connected if and only if A is quasi-hereditary. We apply this result to…

Rigidity dimension is a new homological dimension which is intended to measure the quality of the best resolution of an algebra. In this paper, we determine the rigidity dimensions of self-injective Nakayama agebras A_{n,m} with n simple…

Let $\Lambda$ be an artin algebra, and $\mathcal{V}$ a subset of all simple modules in $\mod\Lambda$. Suppose that $\Lambda/\rad \Lambda$ has finite syzygy type, then the derived dimension of $\Lambda$ is at most…

Repetitiveness in projective and injective resolutions and its influence on homological dimensions are studied. Some variations on the theme of repetitiveness are introduced, and it is shown that the corresponding invariants lead to very…

In this paper we study higher level Deligne--Lusztig representations of reductive groups over discrete valuation rings, with finite residue field $\mathbb{F}_q$. In previous work we proved that, at even levels, these geometrically…

The singularity category of a ring makes only the modules of finite projective dimension vanish among the modules, so the singularity category is expected to characterize a homological property of modules of infinite projective dimension.…

Let $\Lambda$ be an artin algebra. We obtain that $\Lambda$ is syzygy-finite when the radical layer length of $\Lambda$ is at most two; as two consequences, we give a new upper bound for the dimension of the bounded derived category of the…

We construct a finite-dimensional algebra derived equivalent to the example of Kershaw--Rickard. For the Kershaw--Rickard example the delooping level and the sub-derived delooping level are both infinite, while for our algebra both…

We realize certain graded Nakajima varieties of finite Dynkin type as orbit closures of repetitive algebras of Dynkin quivers. As an application, we obtain that the perverse sheaves introduced by Nakajima for describing irreducible…

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…

The geometric and algebraic theory of monomial ideals and multigraded modules is initiated over real-exponent polynomial rings and, more generally, monoid algebras for real polyhedral cones. The main results include the generalization of…

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…

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…