# Mutations for quivers with potentials: Oberwolfach talk, April 2007

@article{Zelevinsky2007MutationsFQ, title={Mutations for quivers with potentials: Oberwolfach talk, April 2007}, author={Andrei Zelevinsky}, journal={arXiv: Rings and Algebras}, year={2007} }

This is an extended abstract of my talk at the Oberwolfach Workshop "Algebraic Groups" (April 22 - 28, 2007). It is based on a joint work with H.Derksen and J.Weyman (arXiv:0704.0649v2 [math.RA]).

## 11 Citations

### Triangulated Categories: Cluster algebras, quiver representations and triangulated categories

- Mathematics
- 2010

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…

### Cohomological Hall algebra, exponential Hodge structures and motivic Donaldson-Thomas invariants

- Mathematics
- 2010

We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack of…

### Quivers with potentials associated to triangulated surfaces

- Mathematics
- 2008

We attempt to relate two recent developments: cluster algebras associated to triangulations of surfaces by Fomin–Shapiro–Thurston, and quivers with potentials (QPs) and their mutations introduced by…

### Quivers with potentials associated to triangulated surfaces, Part II: Arc representations

- Mathematics
- 2009

This paper is a representation-theoretic extension of Part I. It has been inspired by three recent developments: surface cluster algebras studied by Fomin-Shapiro-Thurston, the mutation theory of…

### The noncommutative geometry of the $Y^{p,q}$ quivers

- Mathematics
- 2008

Let A be a Y p,q quiver algebra with center Z. We classify the irreducible representations of A, show that A is homologically homogeneous of global dimension 3, and show that the smooth locus of Z…

### Quivers with potentials associated to triangulated surfaces, Part III: tagged triangulations and cluster monomials

- MathematicsCompositio Mathematica
- 2012

Abstract To each tagged triangulation of a surface with marked points and non-empty boundary we associate a quiver with potential in such a way that whenever we apply a flip to a tagged triangulation…

### Stability structures, motivic Donaldson-Thomas invariants and cluster transformations

- Mathematics
- 2008

We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the category…

### On Arnold’s 14 ‘exceptional’ $ \mathcal{N} = 2 $ superconformal gauge theories

- Mathematics
- 2011

We study the four-dimensional superconformal $ \mathcal{N} = 2 $ gauge theories engineered by the Type IIB superstring on Arnold’s 14 exceptional unimodal singularities (a.k.a. Arnold’s strange…

### On Arnold ’ s 14 ‘ exceptional ’ N = 2 superconformal gauge theories

- Mathematics
- 2013

We study the four–dimensional superconformal N = 2 gauge theories engineered by the Type IIB superstring on Arnold’s 14 exceptional unimodal singularities (a.k.a. Arnold’s strange duality list), thus…

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We provide a quiver-theoretic interpretation of certain smooth complete simplicial fans associated to arbitrary finite root systems in recent work of S. Fomin and A. Zelevinsky. The main properties…

### Quivers with potentials and their representations I: Mutations

- Mathematics
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Abstract.We study quivers with relations given by noncommutative analogs of Jacobian ideals in the complete path algebra. This framework allows us to give a representation-theoretic interpretation of…