Related papers: Characterizing \tau-rigid-finite algebras with rad…

We consider a new correspondence between representations of algebras with radical square zero and representations of species. We show that the stable category of representations of such algebra embeds into the representation category of the…

We determine the derived representation types of algebras with radical square zero and give a description of the indecomposable objects in their bounded derived categories.

We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a…

To an artin algebra with radical square zero, a regular algebra in the sense of von Neumann and a family of invertible bimodules over the regular algebra are associated. These data describe completely, as a triangulated category, the…

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…

In this paper, we complete the classification of representation-finite tensor product algebras in terms of quiver with relations.

Let k a characteristic zero field. We give a characterization for the finite quiver k-algebras, based on double derivations. More precisely, we prove that if an associative and unitary k-algebra have a family of double derivations…

In this paper, we show that for an algebra $\Lambda$ with radical square zero and an indecomposable $\Lambda$-module $M$ such that $\Lambda$ is Gorenstein of finite type or $\tau M$ is $\tau$-rigid, $M$ is $\tau$-rigid if and only if the…

Let $\Lambda$ be a finite dimensional algebra such that $\mathcal{L}_{\Lambda}$ or $\mathcal{R}_{\Lambda}\neq\emptyset$. Then $\Lambda$ is $\tau$-tilting finite if and only if $\Lambda$ is representation-finite.

We show that $\tau$-tilting finite simply connected algebras are representation-finite. Then, some related algebras are considered, including iterated tilted algebras, tubular algebras and so on. We also prove that the $\tau$-tilting…

For algebras with radical square zero, we give a combinatorial description to the Tate-Hochschild cohomology. We compute the Gerstenhaber algebra structure on the Tate-Hochschild cohomology for some classes of such algebras.

We give a new characterization of tilted algebras by the existence of certain special subquivers in their Auslander-Reiten quiver. This result includes the existent characterizations of this kind and yields a way to obtain more tilted…

This paper investigates finiteness conditions for gentle and skew-gentle algebras. First, we prove that a skew-gentle algebra is $\tau$-tilting finite if and only if it is representation-finite, which extends the result for gentle algebras…

We prove that the Crisp and Gow's quiver operation on a finite quiver Q produces a new quiver Q' with fewer vertices, such that the finite dimensional algebras kQ/J^2 and kQ'/J^2 are singularly equivalent. This operation is a general quiver…

We prove that a finite dimensional algebra is $\tau$-tilting finite if and only if it does not admit large silting modules. Moreover, we show that for a $\tau$-tilting finite algebra $A$ there is a bijection between isomorphism classes of…

In [1], finite associative rings wih identity and such that the set of all zero-divisors form and ideal M, called the Jacobson Radical, of cube zero and square non-zero, were constructed for all the characteristics. These rings are…

We determined the $\tau$-tilting finiteness of Schur algebras over an algebraically closed field of arbitrary characteristic, except for a few small cases.

We discuss the finiteness of (two-term) silting objects. First, we investigate new triangulated categories without silting object. Second, one studies two classes of $\tau$-tilting-finite algebras and give the numbers of their two-term…

We show that a gentle algebra over a field is $\tau$-tilting finite if and only if it is representation-finite. The proof relies on the "brick-$\tau$-tilting correspondence" of Demonet-Iyama-Jasso and on a combinatorial analysis.

In this paper we treat the $\tau$-tilting finiteness of biserial (respectively special biserial) algebras over algebraically closed (respectively arbitrary) fields. Inside these families, to compare the notions of representation-finiteness…