We consider a large class of models where an SU(5) gauge symmetry and a FroggattNielsen (FN) Abelian flavor symmetry arise from a quiver gauge theory. Such quiver models are very restrictive and therefore have strong predictive power. In particular, under mild assumptions neutrino mass anarchy is predicted.

The quiver Hopf algebras are classified by means of ramification system with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Nichols type Hopf algebras. 2000 Mathematics Subject Classification: 16W30, 16G10 keywords: Quiver, Hopf algebra, Hopf bimodule, Nichols algebras

We construct bar-invariant Z[q 1 2 ]−bases of the quantum cluster algebra of the Kronecker quiver which are quantum analogues of the canonical basis, semicanonical basis and dual semicanonical basis of the cluster algebra of the Kronecker quiver in the sense of [14],[4] and [11] respectively. As a byproduct, we prove the positivity of the elements in these bases.

A factorization formula for certain automorphisms of a Poisson algebra associated with a quiver is proved, which involves framed versions of moduli spaces of quiver representations. This factorization formula is related to wall-crossing formulas for Donaldson-Thomas type invariants of M. Kontsevich and Y. Soibelman [4].

The purpose of this paper is to describe the topology of the space of strictly stable representations of a quiver with fixed dimension vector, where stability is defined with respect to a given parameter (which may be generic or non-generic). The main result is that the homotopy groups of this space are trivial up to a certain dimension, which depends on the quiver, the choice of dimension vect...

We investigate the Poisson geometry of the Marsden-Weinstein reductions of the moment map associated to the cotangent bundle of the space of representations of a quiver. We show that the stratification by representation type equals the stratification by symplectic leaves. The deformed symplectic quotient singularities spectra of centres of symplectic reflection algebras associated to a wreath p...

This paper concerns preprojective representations of a finite connected valued quiver without oriented cycles. For each such representation, an explicit formula in terms of the geometry of the quiver gives a unique, up to a certain equivalence, shortest (+)-admissible sequence such that the corresponding composition of reflection functors annihilates the representation. The set of equivalence c...

Buch and Fulton [7] conjectured the nonnegativity of the quiver coefficients appearing in their formula for a quiver variety. Knutson, Miller and Shimozono [21] proved this conjecture as an immediate consequence of their “component formula”. We present an alternative proof of the component formula by substituting combinatorics for Gröbner degeneration [21, 20]. We relate the component formula t...

These notes give an introduction to the theory of representations of quivers, in its algebraic and geometric aspects. The main result is Gabriel’s theorem that characterizes quivers having only finitely many isomorphism classes of representations in any prescribed dimension. Résumé. Ces notes donnent une introduction à la théorie des représentations des carquois, sous ses aspects algébrique et ...

The paper studies the interrelationship between coverings of finite directed graphs and gradings of the path algebras associated to the directed graphs. To include gradings of all basic finite-dimensional algebras over an algebraically closed field, a theory of coverings of graphs with relations is introduced. The object of this paper is to relate group gradings on algebras to coverings of a gr...