Related papers: APR tilting modules and graded quivers with potent…

We study silting mutations (Okuyama-Rickard complexes) for selfinjective algebras given by quivers with potential (QPs). We show that silting mutation is compatible with QP mutation. As an application, we get a family of derived…

For a quiver with potential, Derksen, Weyman and Zelevinsky defined a combinatorial transformation - mutations. Mukhopadhyay and Ray, on the other hand, tell us how to compute Seiberg dual quivers for some quivers with potentials through a…

We prove that mutation of cluster-tilting objects in triangulated 2-Calabi-Yau categories is closely connected with mutation of quivers with potentials. This gives a close connection between 2-CY-tilted algebras and Jacobian algebras…

We show that Derksen-Weyman-Zelevinsky's mutations of quivers with potential yield equivalences of suitable 3-Calabi-Yau triangulated categories. Our approach is related to that of Iyama-Reiten and Koszul dual to that of…

This paper generalizes former works of Derksen, Weyman and Zelevinsky about quivers with potentials. We consider semisimple finite-dimensional algebras $E$ over a field $F$, such that $E \otimes_{F} E^{op}$ is semisimple. We assume that $E$…

We generalize Derksen-Weyman-Zelevinsky's theory of quivers with potentials (QPs) to an $H$-based setting by considering quivers with exactly one loop at each vertex, asking the loops to be nilpotent and so attaching a truncated polynomial…

APR tilts for path algebra $kQ$ can be realized as the mutation of the quiver $Q$ in $\mathbb Z Q$ with respect to the translation. In this paper, we show that we have similar results for the quadratic dual of truncations of $n$-translation…

We show that the endomorphism ring of each cluster tilting object in a tubular cluster category is a finite dimensional Jacobian algebra which is tame of polynomial growth. Moreover, these Jacobian algebras are given by a quiver with a…

We consider tilting mutations of a weakly symmetric algebra at a subset of simple modules, as recently introduced by T. Aihara. These mutations are defined as the endomorphism rings of certain tilting complexes of length 1. Starting from a…

We introduce and study potentials, mutations and Jacobian algebras in the framework of tensor algebras associated with symmetrizable dualizing pairs of bimodules on a symmetric algebra over any commutative ground ring. The graded context is…

In this survey article we give a brief account of constructions and results concerning the quivers with potentials associated to triangulations of surfaces with marked points. Besides the fact that the mutations of these quivers with…

We study $2$-representation finite $\mathbb{K}$-algebras obtained from tensor products of tensor algebras of species. In earlier work we computed the higher preprojective algebra of said algebras to be given as Jacobian algebras of certain…

We characterize the marked bordered unpunctured oriented surfaces with the property that all the Jacobian algebras of the quivers with potentials arising from their triangulations are derived equivalent. These are either surfaces of genus g…

Let $A$ be a finite dimensional hereditary algebra over a field $k$ and $A^{(1)}$ the duplicated algebra of $A$. We first show that the global dimension of endomorphism ring of tilting modules of $A^{(1)}$ is at most 3. Then we investigate…

Let $A$ be a finite dimensional algebra over an algebraically closed field $k$. We investigate the structure properties of the endomorphism algebras of semi-tilting $A$-modules, and prove that the endomorphism algebras arising from the…

We attempt to relate two recent developments: cluster algebras associated to triangulations of surfaces by Fomin-Shapiro-Thurston, and quivers with potentials and their mutations introduced by Derksen-Weyman-Zelevinsky. To each ideal…

In arXiv:1506.05880 we gave a generalization of the theory of quivers with potentials introduced by Derksen-Weyman-Zelevinsky, via completed tensor algebras over $S$-bimodules where $S$ is a finite dimensional basic semisimple algebra. In…

A quiver mutation loop is a sequence of mutations and vertex relabelings, along which a quiver transforms back to the original form. For a given mutation loop, we introduce a quantity called a partition q-series. The partition q-series are…

Motivated by work of Barot, Geiss and Zelevinsky, we study a collection of Z-bases (which we call companion bases) of the integral root lattice of a root system of simply-laced Dynkin type. Each companion basis is associated with the quiver…

This paper is a representation-theoretic extension of Part I. It has been inspired by three recent developments: surface cluster algebras studied by Fomin-Shapiro-Thurston, the mutation theory of quivers with potentials initiated by…