相关论文: Derived equivalences between one-branch extensions…
The Nakayama permutations of two derived equivalent, self-injective Artin algebras are conjugate. A different but elementary approach is given to showing that the weak symmetry and self-injectivity of finite-dimensional algebras over an…
In this paper, we construct derived equivalences between certain Nakayama algebras by using the notion of an S-family which is a family of objects in a triangulated category satisfying some axioms.
This present paper is devoted to the study of a class of Nakayama algebras $N_n(r)$ given by the path algebra of the equioriented quiver $\mathbb{A}_n$ subject to the nilpotency degree $r$ for each sequence of $r$ consecutive arrows. We…
Characterizing derived equivalences between algebras via combinatorial structures has recently become a popular topic. In this paper, we study admissible fractional Brauer graph algebras, a new subclass of self-injective special biserial…
We prove that any cyclic Nakayama algebra which is a higher Auslander algebra can be uniquely constructed from Nakayama algebras of smaller ranks by reversing the syzygy filtration process. This creates chains of higher Auslander algebras…
Nakayama automorphisms play an important role in several mathematical branches, which are known to be tough to compute in general. We compute the Nakayama automorphism $\nu$ of any Ore extension $R[x; \sigma, \delta]$ over a polynomial…
Let $A$ be a Koszul Artin-Schelter regular algebra, $\sigma$ a graded automorphism of $A$ and $\delta$ a degree-one $\sigma$-derivation of $A$. We introduce an invariant for $\delta$ called the $\sigma$-divergence of $\delta$. We describe…
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…
A Nakayama algebra with almost separate relations is one where the overlap between any pair of relations is at most one arrow. In this paper we give a derived equivalence between such Nakayama algebras and path algebras of quivers of a…
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.…
We complete the derived equivalence classification of all symmetric algebras of polynomial growth, by solving the subtle problem of distinguishing the standard and nonstandard nondomestic symmetric algebras of polynomial growth up to…
We introduce a new method to construct 4-dimensional Artin-Schelter regular algebras as normal extensions of (not necessarily noetherian) 3-dimensional ones. The method produces large classes of new 4-dimensional Artin-Schelter regular…
We study automorphisms, isomorphisms, and derivations of the incidence algebra $I(X,R)$, where $X$ is preordered set and $R$ is an algebra over some commutative ring $T$.
We generalise two facts about finite dimensional algebras to finite dimensional differential graded algebras. The first is the Nakayama Lemma and the second is that the simples can detect finite projective dimension. We prove two dual…
Let $A$ be a Koszul Artin-Schelter regular algebra and $B=A_P[y_1,y_2;\varsigma,\nu]$ be a graded double Ore extension of $A$ where $\varsigma:A\to M_{2\times 2}(A)$ is a graded algebra homomorphism and $\nu:A\to A^{\oplus 2}$ is a degree…
We present two applications of recent developments in incidence geometry. One is a $\delta$-discretised version of a particular `Elekes--R\'onyai' expander problem. The second application is an incidence estimate addressing the scenario…
This article is concerned with the derived representation theory of certain infinite-dimensional gentle algebras called gentle orders. For a gentle order, we provide a factorization of the derived Nakayama functor, study its fractionally…
We establish and develop a correspondence between certain crystal bases (Kashiwara crystals) and the Coulomb branch of three-dimensional $ \mathcal{N} =4 $ gauge theories. The result holds for simply-laced, non-simply laced and affine…
In this paper, we consider $n$-perforated Yoneda algebras for $n$-angulated categories, and show that, under some conditions, $n$-angles induce derived equivalences between the quotient algebras of $n$-perforated Yoneda algebras. This…