Related papers: Auslander-Reiten quivers and the Coxeter complex

This is the third in a series of papers which give an explicit description of the reconstruction algebra as a quiver with relations; these algebras arise naturally as geometric generalizations of preprojective algebras of extended Dynkin…

We study the Coxeter matrices and the homological quadratic forms of $n$-hereditary algebras within the framework of higher dimensional Auslander--Reiten theory. Let $\Lambda$ be a finite dimensional $n$-hereditary algebra with the Coxeter…

In this paper, we describe a general setting for dimer models on cylinders over Dynkin diagrams which in type A reduces to the well studied case of dimer models on a disc. We prove that all Berenstein--Fomin--Zelevinsky quivers for Schubert…

The connection between simple Lie algebras and their Yangian algebras has a long history. In this work, we construct finite-dimensional representations of Yangian algebras $\mathsf{Y}(\mathfrak{sl}_{n})$ using the quiver approach. Starting…

We study alternating strand diagrams on the disk with an orbifold point. These are quotients by rotation of Postnikov diagrams on the disk, and we call them orbifold diagrams. We associate a quiver with potential to each orbifold diagram,…

This is a survey article for "Handbook of Linear Algebra", 2nd ed., Chapman & Hall/CRC, 2014. An informal introduction to representations of quivers and finite dimensional algebras from a linear algebraist's point of view is given. The…

The notion of an exterior differential system (on a manifold) has recently been extended to the setting of a Lie algebroid. Here, we further develop the theory and we present two versions of the Cartan-K\"ahler theorem in the case where the…

We establish the existence of an IC basis for the generalized Temperley--Lieb algebra associated to a Coxeter system of arbitrary type. We determine this basis explicitly in the case where the Coxeter system is simply laced and the algebra…

We present a method to construct new tilting complexes from existing ones using tensor products, generalizing a result of Rickard. The endomorphism rings of these complexes are generalized matrix rings that are "componentwise" tensor…

A desingularization of arbitrary quiver Grassmannians for representations of Dynkin quivers is constructed in terms of quiver Grassmannians for an algebra derived equivalent to the Auslander algebra of the quiver.

We give analogues of the Auslander correspondence for two classes of triangulated categories satisfying certain finiteness conditions. The first class is triangulated categories with additive generators and we consider their endomorphism…

For quantized universal enveloping algebras we construct weight modules by inducing representations of the centralizer of the Cartan subalgebra in the quantized universal enveloping algebra. The induced modules arising from…

Given a connected non-negative unit form we construct an extended affine Lie algebra by giving a Chevalley basis for it. We also obtain this algebra as a quotient of an algebra defined by means of generalized Serre relations by M. Barot, D.…

We suggest a (conjectural) construction of a basis in the plus part of the affine Lie algebra of type ADE indexed by irreducible components of certain quiver varieties. This construction is closely related to a string-theoretic construction…

Let Q be a finite quiver without oriented cycles, and let k be an algebraically closed field. The main result in this paper is that there is a natural bijection between the elements in the associated Coxeter group W_Q and the cofinite…

Given a quiver, a fixed dimension vector, and a positive integer n, we construct a functor from the category of D-modules on the space of representations of the quiver to the category of modules over a corresponding Gan-Ginzburg algebra of…

We determine the structure of all finite-dimensional self-injective algebras over a field whose Auslander-Reiten quiver admits a hereditary stable slice.

In this article we study the interplay between algebro-geometric notions related to $\pi$-points and structural features of the stable Auslander-Reiten quiver of a finite group scheme. We show that $\pi$-points give rise to a number of new…

We give a bijection between the tilting complexes in the bounded homotopy category of the Auslander algebra of the truncated polynomial ring and ZxB where B is the Artin braid goup of type A with n-1 generators. The tilting complexes have…

Let W be a 2-dimensional right-angled Coxeter group. We characterise such W with linear and quadratic divergence, and construct right-angled Coxeter groups with divergence polynomial of arbitrary degree. Our proofs use the structure of…