A bstract We construct Poisson bracket relations between the operators which generate chiral ring of Coulomb branch certain 3 d $$ \mathcal{N} N = 4 quiver gauge theories. In case where is a free space, ADE Klein singularity, or minimal 2 nilpotent orbit, we explicitly compute brackets generators using either...

We show that the m-cluster category of type Dn is equivalent to a certain geometrically-defined category of arcs in a punctured regular nm − m + 1-gon. This generalises a result of Schiffler for m = 1. We use the notion of the mth power of a translation quiver to realise the m-cluster category in terms of the cluster category. Introduction Let k be a field and Q a quiver of Dynkin type ∆. Let D...

In a k-linear triangulated category (where k is a field) we show that the existence of Auslander-Reiten triangles implies that objects are determined, up to shift, by knowing dimensions of homomorphisms between them. In most cases the objects themselves are distinguished by this information, a conclusion which was also reached under slightly different hypotheses in a theorem of Jensen, Su and Z...

Abstract Let $Q$ be a bipartite quiver, $V$ real representation of $Q$, and $\sigma $ an integral weight orthogonal to the dimension vector $V$. Guided by quiver invariant theoretic considerations, we introduce Brascamp–Lieb (BL) operator $T_{V,\sigma }$ associated $(V,\sigma )$ study its capacity, denoted $\textbf{D}_Q(V, \sigma )$. When is $m$-subspace capacity data intimately related BL cons...

Contents 1. Introduction 1 1.1. Main results 1 1.2. Horn's conjecture and related problems 2 1.3. The quiver method 4 1.4. Organization 5 2. Preliminaries 6 2.1. Basic notions for quivers 6 2.2. Semi-invariants for quiver representations 7 2.3. Representations in general position 8 2.4. The canonical decomposition 9 2.5. The combinatorics of dimension vectors 11 2.6. Perpendicular categories 12...

This paper presents a geometric model of the Auslander–Reiten quiver type A together with stability function for which all indecomposable modules are stable. We also introduce new Catalan object we call maximal almost rigid representation. show that its endomorphism algebra is tilted A. define partial order on set representations and use our to this Cambrian lattice.

the k-vectorspace of outer k-derivations, that is, the quotient of all k-derivations of Λ modulo the inner ones. It has been suspected for some time, and [4] seems to be the earliest reference, that vanishing of the first Hochschild cohomology precludes the existence of oriented cycles in the ordinary quiver. There are various supporting partial results, among them [8, (2.3), (3.2)], [2, (2.2)]...

the k-vectorspace of outer k-derivations , that is, the quotient of all k-derivations of Λ modulo the inner ones. It has been suspected for some time, and [4] seems to be the earliest reference, that vanishing of the first Hochschild cohomology precludes the existence of oriented cycles in the ordinary quiver. There are various supporting partial results, among them [8, (2.3), (3.2)], [2, (2.2)...