Given a presentation of a finitely presented group, there is a natural way to represent the group as the fundamental group of a 2-complex. The first part of this paper demonstrates one possible way to represent a finitely presented algebra S in a similarly compact form. From a presentation of the algebra, we construct a quiver with relations whose path algebra is finite dimensional. When we adj...

Given a presentation of a finitely presented group, there is a natural way to represent the group as the fundamental group of a 2-complex. The first part of this paper demonstrates one possible way to represent a finitely presented algebra S in a similarly compact form. From a presentation of the algebra, we construct a quiver with relations whose path algebra is finite dimensional. When we adj...

We study the proposed duality between the 5-dimensional supergravity/superstiring on AdS3×S and the 2-dimensional N = (0, 4) SCFT defined on the boundary of AdSspace. We construct explicitely the N = (0, 4) SCFT by imposing the “quiver projection” developed by Douglas-Moore [12] on the N = (4, 4) SCFT of symmetric orbifold, which is proposed to be the dual of the 6-dimensional supergravity/supe...

To a finite quiver equipped with a positive integer on each of its vertices, we associate a holomorphic symplectic manifold having some parameters. This coincides with Nakajima’s quiver variety with no stability parameter/framing if the integers attached on the vertices are all equal to one. The construction of reflection functors for quiver varieties are generalized to our case, in which these...

A k-linear triangulated category A is called locally finite provided ∑ X∈indA dimk HomA(X,Y ) < ∞ for any indecomposable object Y in A. It has Auslander–Reiten triangles. In this paper, we show that if a (connected) triangulated category has Auslander–Reiten triangles and contains loops, then its Auslander–Reiten quiver is of the form L̂n: · · · · ̂ n n− 1 2 1 By using this, we prove that the Aus...

Abstract. Given an n-tuple of positive real numbers (α1, . . . , αn), Konno [K2] defines the hyperpolygon space X(α), a hyperkähler analogue of the Kähler variety M(α) parametrizing polygons in R3 with edge lengths (α1, . . . , αn). The polygon space M(α) can be interpreted as the moduli space of stable representations of a certain quiver with fixed dimension vector; from this point of view, X(...

200 NOTICES OF THE AMS VOLUME 52, NUMBER 2 Introduction A quiver is just a directed graph.1 Formally, a quiver is a pair Q = (Q0,Q1) where Q0 is a finite set of vertices and Q1 is a finite set of arrows between them. If a ∈ Q1 is an arrow, then ta and ha denote its tail and its head, respectively. Let us fix a quiver Q and a base field K. Attach a finite dimensional vector space to each vertex ...

Adopting the Mahler measure from number theory, we introduce it to toric quiver gauge theories, and study some of its salient features physical implications. We propose that is a universal for quiver, encoding dynamics with monotonic behaviour along so-called flow including two special points at isoradial tropical limits. Along flow, amoeba, geometry, provides geometric interpretations quiver. ...

The notion of mixed representations of quivers can be derived from ordinary quiver representations by considering the dual action of groups on “vertex” vector spaces together with the usual action. A generating system for the algebra of semi-invariants of mixed representations of a quiver is determined. This is done by reducing the problem to the case of bipartite quivers of the special form an...