Related papers: Representations of quivers and mixed graphs

Given a graph E we define E-algebraic branching systems, show their existence and how they induce representations of the associated Leavitt path algebra. We also give sufficient conditions to guarantee faithfulness of the representations…

In this paper the main results in arXiv:0901.3179v3, related to the matrix representation of polynomial maps, are restated in traditional way of linear algebra assuming that variable vectors are presented as column vectors. Some new results…

Dynamical systems often admit geometric properties that must be taken into account when studying their behaviour. We show that many such properties can be encoded by means of quiver representations. These properties include classical…

We describe the "generic" part of the character ring of general linear groups over a finite field in terms of quiver representations.

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…

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…

Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…

We propose a definition of expander representations of quivers, generalizing dimension (or linear algebra) expanders, as a qualitative refinement of slope stability. We prove existence of uniform expander representations for any wild quiver…

Quivers (directed graphs) and species (a generalization of quivers) and their representations play a key role in many areas of mathematics including combinatorics, geometry, and algebra. Their importance is especially apparent in their…

We give an overview of combinatorial methods to represent 3D data, such as graphs and meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and…

A unitary (Euclidean) representation of a quiver is given by assigning to each vertex a unitary (Euclidean) vector space and to each arrow a linear mapping of the corresponding vector spaces. We recall an algorithm for reducing the matrices…

We count singular vector tuples of a system of tensors assigned to the edges of a directed hypergraph. To do so, we study the generalisation of quivers to directed hypergraphs. Assigning vector spaces to the nodes of a hypergraph and…

The application of the max-algebra to describe queueing systems by both linear scalar and vector equations is discussed. It is shown that these equations may be handled using ordinary algebraic manipulations. Examples of solving the…

We develop a theory of sesquilinear forms over finite fields, investigating their representations via polynomials and coefficient matrices, along with classification results for these forms. Through their connection to quadratic forms, we…

It is well-known that a quiver Q of type A_n is representation-finite, and that its indecomposable representations are thin (all Jordan-Hoelder multiplicities are 0 or 1). By now, various methods of proof are known. The aim of this note is…

In this paper, we complete the classification of representation-finite tensor product algebras in terms of quiver with relations.

As it is known, finitely presented quivers correspond to Dynkin graphs (Gabriel, 1972) and tame quivers -- to extended Dynkin graphs (Donovan and Freislich, Nazarova, 1973). In the article "Locally scalar reresentations of graphs in the…

On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…

Suppose a finite group acts on a scheme X and a finite-dimensional Lie algebra g. The corresponding equivariant map algebra is the Lie algebra M of equivariant regular maps from X to g. We classify the irreducible finite-dimensional…

The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…