We study the matrix models that describe the BPS bound states of branes arising from the quiver picture of the derived category. These theories have a topological partition function that localizes to the Euler character of the anti-ghost bundle over the classical BPS moduli space. We examine the effective internal geometry of D6/D2 bound states in the local vertex geometry, using BPS 0-brane pr...

We call a 2-Calabi-Yau triangulated category a cluster category if its cluster-tilting subcategories form a cluster structure as defined in [4]. In this paper, we show that the canonical orbit category of the bounded derived category of finite dimensional representations of a quiver without infinite paths of type A∞ or A∞ is a cluster category. Moreover, for a cluster category of type A∞, we gi...

In a previous paper, Auslander-Reiten triangles and quivers were introduced into algebraic topology. This paper shows that over a Poincaré duality space, each component of the Auslander-Reiten quiver is isomorphic to ZA∞.

First, for a general Krull-Schmidt category, we provide criteria for an Auslander-Reiten component with sections to be standard. Specializing to the category of finitely presented representations of a strongly locally finite quiver and its bounded derived category, we obtain many new types of standard Auslander-Reiten components. Finally, specialized to the module category of a finite-dimension...

This paper characterizes the injective and projective objects in the category of directed multigraphs, or quivers. Further, the injective envelope and projective cover of any quiver in this category is constructed.

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 complex integrable systems on quiver varieties associated with the cyclic quiver, and prove their superintegrability by explicitly constructing first integrals. interpret them as rational Calogero-Moser endowed internal degrees of freedom called spins. They encompass usual in type $A_{n-1}$ $B_n$, well generalisations introduced Chalykh Silantyev connection multicomponent KP hierarchy....

In this work we obtain a version of the Procesi-Rasmyslov Theorem for the algebra of semi-invariants of representations of an arbitrary quiver with dimension vector (2, 2, . . . , 2).