Related papers: On maximal green sequence for quivers arising from…

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…

For a symmetrizable Kac-Moody Lie algebra $\mathfrak{g}$, we construct a family of weighted quivers $Q_m(\mathfrak{g})$ ($m \geq 2$) whose cluster modular group $\Gamma_{Q_m(\mathfrak{g})}$ contains the Weyl group $W(\mathfrak{g})$ as a…

A new version of application Pauli-Villars regularized Green functions in the quantum field theory using higher derivatives is proposed. In this version the regularizing mass $M$ is large but finite. Our approach is demonstrated and…

We classify all mutation-finite quivers with real weights. We show that every finite mutation class not originating from an integer skew-symmetrizable matrix has a geometric realization by reflections. We also explore the structure of…

An upper bound on degrees of elements of a minimal generating system for invariants of quivers of dimension (2,...,2) is established over a field of arbitrary characteristic and its precision is estimated. The proof is based on the…

This paper introduces a class of smooth projective varieties that generalise and share many properties with partial flag varieties of type A. The quiver flag variety M_\vartheta(Q,r) of a finite acyclic quiver Q (with a unique source) and a…

Let Q be a finite quiver without sources, and A be the corresponding algebra with radical square zero. We construct an explicit compact generator for the homotopy category of acyclic complexes of projective A-modules. We call such a…

Exceptional sequences are certain ordered sequences of quiver representations. We use noncrossing edge-labeled trees in a disk with boundary vertices (expanding on T. Araya's work) to classify exceptional sequences of representations of Q,…

We study the Ext modules in the category of left modules over a twisted algebra of a finite quiver over a ringed space $(X,\mathcal O_X)$, allowing for the presence of relations. We introduce a spectral sequence which relates the Ext…

We construct a special embedding of the translation quiver $\mathbb{Z}Q$ in the three-dimensional affine space $\mathbb{R}^{3}$ where $Q$ is a finite connected acyclic quiver and $\mathbb{Z}Q$ contains a local slice whose quiver is…

We introduce a new method for expanding an abelian category and study it using recollements. In particular, we give a criterion for the existence of cotilting objects. We show, using techniques from noncommutative algebraic geometry, that…

We consider quivers/skew-symmetric matrices under the action of mutation (in the cluster algebra sense). We classify those which are isomorphic to their own mutation via a cycle permuting all the vertices, and give families of quivers which…

We show that there exists a cubic threefold defined by an invertible polynomial that, when quotiented by the maximal diagonal symmetry group, has a derived category which does not have a full exceptional collection consisting of line…

For the ultradifferentiable weight sequence setting it is known that the Borel map which assigns to each function the infinite jet of derivatives (at 0) is surjective onto the corresponding weighted sequence class if and only if the…

We initiate a study of the dependence on the choice of ground ring on the question of whether a cluster algebra is equal to its upper cluster algebra. A condition for when there is equality of the cluster algebra and upper cluster algebra…

For an interval finite quiver $Q$, we introduce a class of flat representations. We classify the indecomposable projective objects in the category $\mathrm{rep}(Q)$ of pointwise finite dimensional representations. We show that an object in…

The present paper is related to a conjecture made by Green and Lazarsfeld concerning 1-linear syzygies of curves embedded by complete linear systems of sufficiently large degrees. Given a smooth, irreducible, complex, projective curve $X$,…

We study the category of graded finite-dimensional representations of the polynomial current algebra associated to a simple Lie algebra. We prove that the category has enough injectives and compute the graded character of the injective…

A cluster is a finite set of generators of a cluster algebra. The Laurent Phenomenon of Fomin and Zelevinsky says that any element of a cluster algebra can be written as a Laurent polynomial in terms of any cluster. The upper cluster…

We provide a combinatorial description of morphisms in the coherent sheaf category ${\rm coh}\mbox{-}\mathbb{X}(p,q)$ over weighted projective line of type $(p,q)$ via a marked annulus. This leads to a geometric realization of exceptional…