Related papers: Representations of quivers, their generalizations …

We describe presentations of braid groups of type $A$ arising from coloured quivers of mutation type $A$. We show that these can be interpreted geometrically as generalised triangulations of regular polygons.

We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between…

We characterize the generating function of the number of representations described in the title in terms of the theory of modular forms. Appealing to this characterization we obtain explicit formulas for the representation numbers as…

Stretching the parameters of a Littlewood-Richardson coefficient of value 2 by a factor of n results in a coefficient of value n+1. We give a geometric proof of a generalization for representations of quivers.

We give two generalizations of Kac's Theorem on representations of quivers. One is to representations of equipped graphs by relations, in the sense of Gelfand and Ponomarev. The other is to representations of quivers in which certain of the…

The input and output algebras of an infinite qubit system and their representations are described.

Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.

This article develops an alcove geometric approach to the representation theory of certain affine Hecke algebra quotients generalizing the blob algebra; and gives an exposition of some new representations of these algebras.

In this paper I consider the polymorpism of representations of universal algebra and tensor product of representations of universal algebra.

This is a concise overview of the definitions and properties of the linking number and its higher-order generalization, Milnor invariants.

The Frobenius-Perron theory of an endofunctor of a category was introduced in recent years [12, 13]. We apply this theory to monoidal (or tensor) triangulated structures of quiver representations.

In this work we obtain a version of the Procesi-Rasmyslov Theorem for the algebra of semi-invariants of representations of an arbitrary quiver with dimension vector (2,2,...,2).

We introduce the notion of mc-biquandles, algebraic structures which have possibly distinct biquandle operations at single-component and multi-component crossings. These structures provide computable homset invariants for classical and…

The connections amongst (1) quivers whose representation varieties are Calabi-Yau, (2) the combinatorics of bipartite graphs on Riemann surfaces, and (3) the geometry of mirror symmetry have engendered a rich subject at whose heart is the…

Translated into the language of representations of quivers, a challenge in matrix pencil theory is to find sufficient and necessary conditions for a Kronecker representation to be a subfactor of another Kronecker representation in terms of…

Biquandle brackets define invariants of classical and virtual knots and links using skein invariants of biquandle-colored knots and links. Biquandle coloring quivers categorify the biquandle counting invariant in the sense of defining…

In a series of papers published in this Journal (J. Math. Phys.), a discussion was started on the significance of a new definition of projective representations in quaternionic Hilbert spaces. The present paper gives what we believe is a…

We define a functor which gives the "global rank of a quiver representation" and prove that it has nice properties which make it a generalization of the rank of a linear map. We demonstrate how to construct other "rank functors" for a…

The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…

We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…