Starting from the N = 2 SYM4 quiver theory living on wrapped NiD5 branes around S 2 i spheres of deformed ADE fibered Calabi-Yau threefolds (CY3) and considering deformations using massive vector multiplets, we explicitly build a new class of N = 1 quiver gauge theories. In these models, the quiver gauge group ∏ i U (Ni) is spontaneously broken down to ∏ i SU (Ni) and Kahler deformations are sh...

This paper proves that every projective toric variety is the fine moduli space for stable representations of an appropriate bound quiver. To accomplish this, we study the quiver Q with relations R corresponding to the finite-dimensional algebra End (⊕ r i=0 Li ) where L := (OX , L1, . . . , Lr) is a list of line bundles on a projective toric variety X . The quiver Q defines a unimodular, projec...

It is shown that rational points over finite fields of moduli spaces of stable quiver representations are counted by polynomials with integer coefficients. These polynomials are constructed recursively using an identity in the Hall algebra of a quiver.

We provide a quiver setting for quasi-Hopf algebras, generalizing the Hopf quiver theory. As applications we obtain some general structure theorems, in particular the quasi-Hopf analogue of the Cartier theorem and the Cartier-Gabriel decomposition theorem.

In this work, we show that neural networks can be represented via the mathematical theory of quiver representations. More specifically, prove a network is representation with activation functions, object represent using quiver. Furthermore, quivers gently adapt to common concepts such as fully connected layers, convolution operations, residual connections, batch normalization, pooling operation...

We define and study virtual representation spaces for vectors having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual semi-invariants and prove that they satisfy the three basic theorems: the First Fundamental Theorem, the Saturation Theorem and the Canonical Decomposition The...

In particular, Q has finitely many indecomposables if and only if the underlying graph of Q is a disjoint union of copies of type ADE graphs. In this case, the above theorem is true for any field. Hence we can identify the isomorphism class of a representation over a Dynkin quiver with a function from the positive roots of ∆ to the nonnegative integers. The path algebra of Q is hereditary, so E...

We define and study virtual representation spaces having both positive and negative dimensions at the vertices of a quiver without oriented cycles. We consider the natural semi-invariants on these spaces which we call virtual semi-invariants and prove that they satisfy the three basic theorems: the First Fundamental Theorem, the Saturation Theorem and the Canonical Decomposition Theorem. In the...

We show that variants of the classical reflection functors from quiver representation theory exist in any abstract stable homotopy theory, making them available for example over arbitrary ground rings, for quasicoherent modules on schemes, in the differential-graded context, in stable homotopy theory as well as in the equivariant, motivic, and parametrized variant thereof. As an application of ...

This is a contribution to the project of quiver approaches to quasi-quantum groups initiated in [13]. We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations. This leads to a theoretic classification of graded pointed Majid algebras over path coalgebras, or equivalently cofree pointed coalgebras, and helps to provide a projective representation-theoretic ...