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Quivers with potentials associated to triangulated surfaces, part IV: Removing boundary assumptions
Quivers potentials triangulated surfaces Removing boundary assumptions Combinatorics
2012/6/30
We prove that the quivers with potentials associated by the author to ideal triangulations of punctured surfaces with empty boundary are non-degenerate, provided the number of punctures is 1 or greate...
Representations of quivers with automorphisms over finite fields
quiver with automorphism hereditary algebra representation
2011/9/28
Let ${mathbb F}_q$ be the finite field of $q$ elements and $k$ be its algebraic closure. Let $Q$ be a quiver with automorphism $sigma$. In this survey we focus on the study of modules over the ${mathb...
Category equivalences involving graded modules over path algebras of quivers
Category equivalences path algebras of quivers Rings and Algebras
2011/9/14
Abstract: Let kQ be the path algebra of a quiver Q with its standard grading. We show that the category of graded kQ-modules modulo those that are the sum of their finite dimensional submodules, QGr(k...
Categorification of the Fibonacci numbers using representations of quivers
Categorification of the Fibonacci numbers representations of quivers Representation Theory
2011/8/31
Abstract: In a previous paper we have presented a partition formula for the even-index Fibonacci numbers using the preprojective representations of the 3-Kronecker quiver and its universal cover, the ...
Quivers of sections on toric Deligne-Mumford stacks
Quivers of sections toric Deligne-Mumford stacks
2011/1/21
Starting from a collection of line bundles on a smooth projective toric DM stack,we give a stacky analogue of the classical linear series construction. We apply our construction to recover the finite ...
Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
Instantons Quivers Noncommutative Donaldson-Thomas Theory
2011/3/2
We construct noncommutative Donaldson{Thomas invariants associated with abelian orbifold
singularities by analysing the instanton contributions to a six-dimensional topological gauge
theory.
Geometric approach to Hall algebra of representations of Quivers over local ring
Quantum generalized Kac-Moody algebra Hall algebra quiver local ring
2011/2/25
The category of representations of a Dynkin quiver over local ring R = k[t]/(tn) is not hereditary any more. The Hall algebra defined on this category doesn’t have a well defined coalgebraic structure...
We investigate the connection between representations of posets and those of the corresponding (bound) quivers. As far as quivers are concerned, we concentrate on unitarizable representations which ar...
Coloured quivers for rigid objects and partial triangulations: The unpunctured case
Coloured quivers rigid objects partial triangulations unpunctured case
2011/2/28
We associate a coloured quiver to a rigid object in a Hom-finite 2-Calabi–Yau triangulated category and to a partial triangulation on a marked (unpunctured) Riemann surface.
Symmetric quivers, invariant theory, and saturation theorems for the classical groups
Symmetric quivers invariant theory saturation theorems for the classical groups
2010/12/7
Let G denote either a special orthogonal group or a symplectic group defined over the complex
numbers. We prove the following saturation result for G: given dominant weights λ1, . . . , λr
such that...
Relative homological algebra in categories of representations of infinite quivers
cover envelope torsion free flat representations of a quiver
2010/11/26
In the first part of this paper, we prove the existence of torsion
free covers in the category of representations of quivers, (Q,R-Mod),for a wide class of quivers included in the class of the so-cal...
Indecomposable representations of the Kronecker quivers
Indecomposable representations Kronecker quivers
2010/12/14
Let k be a field and the n-Kronecker algebra, this is the path algebra of the quiver with 2 vertices, a source and a sink, and n arrows from the source to the sink. It is wellknown
that the dimensi...
Idempotents in representation rings of quivers
Idempotents representation rings of quivers
2010/11/26
For an acyclic quiver Q, we solve the Clebsch-Gordan problem for the projective representations by computing the mul-tiplicity of a given indecomposable projective in the tensor product of two indecom...
Mutation-Periodic Quivers, Integrable Maps and Associated Poisson Algebras
Integrable Maps Associated Poisson Algebras
2010/4/2
We consider a class of map, recently derived in the context of cluster mutation. In this paper we start with a brief review of the quiver context, but then move onto a discussion of a related Poisson ...
Counting BPS Operators in Gauge Theories- Quivers, Syzygies and Plethystics
Counting BPS Operators Gauge Theories- Quivers Syzygies Plethystics
2018/4/20
We develop a systematic and efficient method of counting single-trace and multi-trace BPS operators for world-volume gauge theories of N D-brane probes, for both N → ∞ and finite N. The techniques are...