Related papers: Representations of quivers and mixed graphs

We define elliptic generalization of W-algebras associated with arbitrary quiver using the formalism of arXiv:1512.08533 applied to six-dimensional quiver gauge theory compactified on elliptic curve.

This book is mainly an exposition of the author's works and his joint works with his former students on explicit representations of finite-dimensional simple Lie algebras, related partial differential equations, linear orthogonal algebraic…

Using linear algebraic methods we show that every (possibly infinite-dimensional) representation of a quiver with underlying graph $A_{\infty, \infty}$ is Krull-Schmidt, as long as the arrows in the quiver eventually point outward.

In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…

In this paper we prove an identity in terms of generating functions which enables us to calculate the numbers of isomorphism classes of absolutely indecomposable semistable representations of quivers over finite fields.

Let $Q$ be a finite quiver without oriented cycles and $k$ an algebraically closed field.In this paper we establish a connection between cluster algebras and the representation theory of the path algebra $kQ$, in terms of the spectral…

The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory…

We introduce a notion of representation for a class of generalised quivers known as Coxeter quivers. These representations are built using fusion categories associated to $U_q(\mathfrak{s}\mathfrak{l}_2)$ at roots of unity and we show that…

Covering theory is an important tool in representation theory of algebras, however, the results and the proofs are scattered in the literature. We give an introduction to covering theory at a level as elementary as possible.

In \cite{FT19}, Finkelberg and Tsymbaliuk introduced the notion of shifted quantum affine algebras and described their role in the study of quantized Coulomb branches associated to certain 3D $N = 4$ quiver gauge theories. We describe a new…

We use pluriharmonic maps to study representations of fundamental groups of algebraic manifolds. This approach is functorial in the sense that the restriction of such a map to a fiber of a fibration remains pluriharmonic, and on this basis,…

The $n$-slice algebra is introduced as a generalization of path algebra in higher dimensional representation theory. In this paper, we give a classification of $n$-slice algebras via their $(n+1)$-preprojective algebras and the trivial…

Theory of representations of F-algebra is a natural development of the theory of F-algebra. Exploring of morphisms of the representation leads to the concepts of generating set and basis of representation. In the book I considered the…

We consider $m$-cluster tilted algebras arising from quivers of Euclidean type and we give necessary and sufficient conditions for those algebras to be representation finite. For the case $\widetilde{A}$, using the geometric realization, we…

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 classify a class of complex representations of an arbitrary Coxeter group via characters of the integral homology of certain graphs. Such representations can be viewed as a generalization of the geometric representation and correspond to…

Natural linear and coalgebra transformations of tensor algebras are studied. The representations of certain combinatorial groups are given. These representations are connected to natural transformations of tensor algebras and to the groups…

We study bilinear embedding models for the task of multi-relational link prediction and knowledge graph completion. Bilinear models belong to the most basic models for this task, they are comparably efficient to train and use, and they can…

Graphs arise naturally in many real-world applications including social networks, recommender systems, ontologies, biology, and computational finance. Traditionally, machine learning models for graphs have been mostly designed for static…

Motivated by problems in the neural networks setting, we study moduli spaces of double framed quiver representations and give both a linear algebra description and a representation theoretic description of these moduli spaces. We define a…