Related papers: Jacobian algebras with periodic module category an…

We show that the category of projective modules over a graded commutative ring admits a triangulation with respect to module suspension if and only if the ring is a finite product of graded fields and exterior algebras on one generator over…

We study tensor structures on (Rep G)-module categories defined by actions of a compact quantum group G on unital C*-algebras. We show that having a tensor product which defines the module structure is equivalent to enriching the action of…

Let $A$ be a $k$-algebra where $k$ is an algebraically closed field and $G$ be a finite abelian group for which the characteristic of $k$ does not divide $|G|$. If $G$ acts on $A$ by $k$-algebra automorphisms then the action induces a…

Let $d$ be a positive integer. In a previous article we established a bijective correspondence between the following classes of objects, considered up to the appropriate notion of equivalence: differential graded algebras with…

In this paper we study an algebra that naturally combines two familiar operations in scattering amplitudes: computations of volumes of polytopes using triangulations and constructions of canonical forms from products of smaller ones. We…

A version of Auslander theorem is proven for the following classes of noncommutative algebras: (a) noetherian PI local (or connected graded) algebras of finite injective dimension, (b) universal enveloping algebras of finite dimensional Lie…

We consider a class of relative $n$-Calabi--Yau dg-algebras, referred to as relative Ginzburg algebras, associated with marked surfaces equipped with a decomposition into $n$-gons ($n$-angulation). We relate their derived categories to the…

We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians ${\rm Gr}(k,n)$. A finite cluster algebra provides a natural triangulation for the…

We give a linear algebraic classification of Auslander regular acyclic monomial algebras via the Bruhat factorisation of the Coxeter matrix. Namely, we show under mild assumptions that a monomial acyclic quiver algebra is Auslander regular…

We characterize mutation-finite cluster algebras of rank at least 3 using positive semi-definite quadratic forms. In particular, we associate with every unpunctured bordered surface a positive semi-definite quadratic space $V$, and with…

Let $\mathcal{A}$ be an additive $k-$category and $\mathbf{C}_{\equiv m}(\mathcal{A})$ be the category of $m-$periodic objects. For any integer $m>1$, we study conditions under which the compression functor ${\mathcal F}_m…

Let $(\mathscr{C},\mathbb{E},\mathfrak{s})$ be an ${\rm Ext}$-finite, Krull-Schmidt and $k$-linear $n$-exangulated category with $k$ a commutative artinian ring. In this note, we define two additive subcategories $\mathscr{C}_r$ and…

Higher Auslander algebras were introduced by Iyama generalizing classical concepts from representation theory of finite dimensional algebras. Recently these higher analogues of classical representation theory have been increasingly studied.…

Let Q be a Dynkin quiver of type A. The bounded derived category of the path algebra of Q has an autoequivalence given by the composition of the Auslander-Reiten translate and the square of the shift functor. We classify the maximal rigid…

We provide a combinatorial algorithm for constructing the stable Auslander-Reiten component containing a given indecomposable module of a symmetric special biserial algebra using only information from its underlying Brauer graph. We also…

We develop a novel combinatorial perspective on the higher Auslander algebras of type $\mathbb{A}$, a family of algebras arising in the context of Iyama's higher Auslander-Reiten theory. This approach reveals interesting simplicial…

From the viewpoint of higher dimensional Auslander-Reiten theory, we introduce a new class of finite dimensional algebras of global dimension n, which we call n-representation infinite. They are a certain analog of representation infinite…

To each triangulation of any surface with marked points on the boundary and orbifold points of order three, we associate a quiver (with loops) with potential whose Jacobian algebra is finite dimensional and gentle. We study the stability…

We describe what it means for an algebra to be internally d-Calabi-Yau with respect to an idempotent. This definition abstracts properties of endomorphism algebras of (d-1)-cluster-tilting objects in certain stably (d-1)-Calabi-Yau…

Let $\Lambda$ be a finite dimensional Auslander algebra. For a $\Lambda$-module $M$, we prove that the projective dimension of $M$ is at most one if and only if the projective dimension of its socle soc\,$M$ is at most one. As an…