Related papers: Leavitt path algebras and their representations

Motivated by the study of traces on graph $C^*$-algebras, we consider traces (additive, central maps) on Leavitt path algebras, the algebraic counterparts of graph $C^*$-algebras. In particular, we consider traces which vanish on nonzero…

Let $K$ be any field, and let $E$ be a finite graph with the property that every vertex in $E$ is the base of at most one cycle (we say such a graph satisfies Condition (AR)). We explicitly construct the injective envelope of each simple…

This article is the first of two where we investigate to what extent homotopy invariant, excisive and matrix stable homology theories help one distinguish between the Leavitt path algebras $L(E)$ and $L(F)$ of graphs $E$ and $F$ over a…

The trace on matrix rings, along with the augmentation map and Kaplansky trace on group rings, are some of the many examples of linear functions on algebras that vanish on all commutators. We generalize and unify these examples by studying…

We study two classes of inverse semigroups built from directed graphs, namely graph inverse semigroups and a new class of semigroups that we refer to as Leavitt inverse semigroups. These semigroups are closely related to graph…

We study, from a combinatorial viewpoint, the quantized coordinate ring of mxn matrices over an infinite field K (also called quantum matrices) and its torus-invariant prime ideals. The first part of this paper shows that this algebra,…

Let G be a Lie group, $g = Lie(G)$ - its Lie algebra, $g*$ - the dual vector space and $\widehat G$ - the set of equivalence classes of unitary irreducible representations of $G$. The orbit method [1] establishes a correspondence between…

Let E be an arbitrary directed graph and let K be any field. It is shown that the Leavitt path algebra A of the graph E over the field K is a Zorn ring if and only if the graph E satisfies the Condition (L), that is, every cycle in E has an…

Representations of equipped graphs were introduced by Gelfand and Ponomarev; they are similar to representation of quivers, but one does not need to choose an orientation of the graph. In a previous article we have shown that, as in Kac's…

We characterize pairs (Q,d) consisting of a quiver Q and a dimension vector d, such that over a given algebraically closed field k there are infinitely many representations of Q of dimension vector d. We also present an application of this…

We continue the study of $L^p$-operator algebras associated with directed graphs initiated by Corti\~nas and Rodr\'iguez, and we establish $L^p$-analogs of both the gauge-invariant and the Cuntz-Krieger uniqueness theorems. The first of…

In this paper, we initiate the study of Leavitt path algebra over Kronecker square of a quiver and show the similarities and contrasts in the properties of Leavitt path algebra over a quiver and its Kronecker square. Furthermore, we discuss…

We introduce an infinite family of quiver representation-valued invariants of classical, virtual and surface-knots and links associated to a choice of finite biquandle, commutative unital ring, biquandle module and set of biquandle…

We develop new techniques for the construction and classification of representations of row-finite and locally convex higher-rank graph C*-algebras O. This class includes Cuntz--Krieger algebras associated to row-finite directed graphs. Our…

The algebraic structures known as {\it Leavitt path algebras} were initially developed in 2004 by Ara, Moreno and Pardo, and almost simultaneously (using a different approach) by the author and Aranda Pino. During the intervening decade,…

We introduce and study a new inverse semigroup associated to a separated graph $(E,C)$, which we call the \emph{Leavitt inverse semigroup}. This semigroup is obtained as a quotient of the separated graph inverse semigroup…

We consider generalized $\Lambda$-structures on algebras and schemes over the ring of integers $\mathit{O}_K$ of a number field $K$. When $K=\mathbb{Q}$, these agree with the $\lambda$-ring structures of algebraic K-theory. We then study…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

A group graded $K$-algebra $A=\bigoplus\limits_{g\in G} A_g$ is called "locally finite" if $\dim_K A_g < \infty$ for every $g\in G$. We characterise the weighted graphs $(E,w)$ for which the weighted Leavitt path algebra $L_K(E,w)$ is…

In this note we prove that the algebras $L_K(E)$ and $KE$ have the same entropy. Entropy is always referred to the standard filtrations in the corresponding kind of algebra. The main argument leans on (1) the holomorphic functional…