Related papers: Cluster Complexes via Semi-Invariants

We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their non-projective indecomposable modules are…

This is an introduction to some aspects of Fomin-Zelevinsky's cluster algebras and their links with the representation theory of quivers and with Calabi-Yau triangulated categories. It is based on lectures given by the author at summer…

We show how quiver representations and their invariant theory natu- rally arise in the study of some moduli spaces parametrizing bundles dened on an algebraic curve, and how they lead to ne results regarding the geometry of these spaces.

A pathway from one vertex of a quiver to another is a reduced path. We modify the classical definition of quiver representations and we prove that semi-invariant polynomials for filtered quiver representations come from diagonal entries if…

For a quasi-projective scheme M which carries a perfect obstruction theory, we construct the virtual cobordism class of M. If M is projective, we prove that the corresponding Chern numbers of the virtual cobordism class are given by…

We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver…

Integral cluster categories of acyclic quivers have recently been used in the representation-theoretic approach to quantum cluster algebras. We show that over a principal ideal domain, such categories behave much better than one would…

Any moduli space of representations of a quiver (possibly with oriented cycles) has an embedding as a dense open subvariety into a moduli space of representations of a bipartite quiver having the same type of singularities. A connected…

We show that the mutation class of a finite quiver without oriented cycles is finite if and only is the quiver is either Dynkin, extended Dynkin or has at most two vertices.

We sketch the construction of a quantum model of 3 dimensional de Sitter space, based on the Covariant Entropy Principle and the observation that semi-classical physics suggests the possibility of a consistent theory of a finite number of…

We study the representation theory of Dynkin quivers of type A in abstract stable homotopy theories, including those associated to fields, rings, schemes, differential-graded algebras, and ring spectra. Reflection functors, (partial)…

We introduce quiver representation-valued invariants of oriented virtual knots and links associated to a choice of finite virtual biquandle, abelian group, set of virtual Boltzmann weights, commutative unital ring and set of virtual…

We define the notion of an invariant function on a cluster ensemble with respect to an action of the cluster modular group on its associated function fields. We realize many examples of previously studied functions as elements of this type…

We suggest a geometrical approach to the semi-invariants of quivers based on Luna's slice theorem and the Luna-Richardson theorem. The locally semi-simple representations are defined in this spirit but turn out to be connected with stable…

The categories with noninvertible morphisms are studied analogously to the semisupermanifolds with noninvertible transition functions. The concepts of regular n-cycles, obstruction and the regularization procedure are introduced and…

Let $(Q,\sigma)$ be a symmetric quiver, where $Q=(Q_0,Q_1)$ is a finite quiver without oriented cycles and $\sigma$ is a contravariant involution on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form $<,>$ on…

We first study the (canonical) orbit category of the bounded derived category of finite dimensional representations of a quiver with no infinite path, and we pay more attention on the case where the quiver is of infinite Dynkin type. In…

We show that a finite, connected quiver Q without oriented cycles is a Dynkin or Euclidean quiver if and only if all orbit semigroups of representations of Q are saturated.

This is my PhD thesis supervised by Professor Jerzy Weyman. A symmetric quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The involution allows…

The issue of how to deal with the modular transformations -- large diffeomorphisms -- in (2+1)-quantum gravity on the torus is discussed. I study the Chern-Simons/connection representation and show that the behavior of the modular…