Related papers: Regularity conditions for arbitrary Leavitt path a…

An introduction to Leavitt path algebras of arbitrary directed graphs is presented, and direct limit techniques are developed, with which many results that had previously been proved for countable graphs can be extended to uncountable ones.…

Let $K$ be a fixed field. We attach to each column-finite quiver $E$ a von Neumann regular $K$-algebra $Q(E)$ in a functorial way. The algebra $Q(E)$ is a universal localization of the usual path algebra $P(E)$ associated with $E$. The…

The aim of this work is the description of the isomorphism classes of all Leavitt path algebras coming from graphs satisfying Condition (Sing) with up to three vertices. In particular, this classification recovers the one achieved by Abrams…

Given an arbitrary graph E and any field K, a new class of simple left modules over the Leavitt path algebra L of the graph E over K is constructed by using vertices that emit infinitely many edges. The corresponding annihilating primitive…

We realize Leavitt ultragraph path algebras as partial skew group rings. Using this realization we characterize artinian ultragraph path algebras and give simplicity criteria for these algebras.

Let E be an arbitrary graph and K be any field. For every non-graded ideal I of the Leavitt path algebra L_{K}(E), we give an explicit description of the generators of I. Using this, we show that every finitely generated ideal of L_{K}(E)…

Let $E$ be an arbitrary directed graph and let $L$ be the Leavitt path algebra of the graph $E$ over a field $K$. The necessary and sufficient con- ditions are given to assure the existence of a maximal ideal in $L$ and also the necessary…

Refining an idea of Rosenmann and Rosset we show that the now widely studied classical Leavitt algebra $L_K(1,n)$ over a field $K$ is a ring of right quotients of the unital free associative algebra of rank $n$ with respect to the perfect…

For a field $F$ of characteristic not 2 and a directed row-finite graph $\Gamma$ let $L(\Gamma)$ be the Leavitt path algebra with the standard involution $*.$ We study the Lie algebra $K=K(L(\Gamma),*)$ of $*-$skew-symmetric elements and…

In this paper we address the classification problem for purely infinite simple Leavitt path algebras of finite graphs over a field $\ell$. Each graph $E$ has associated a Leavitt path $\ell$-algebra $L(E)$. There is an open question which…

In this paper, we describe the $K$-module $HH^1(L_K(\Gamma))$ of outer derivations of the Leavitt path algebra $L_K(\Gamma)$ of a row-finite graph $\Gamma$ with coefficients in an associative commutative ring $K$ with unit. We give an…

For a weighted graph $E$, we construct representation graphs $F$, and consequently, $L_K(E)$-modules $V_F$, where $L_K(E)$ is the Leavitt path algebra associated to $E$, with coefficients in a field $K$. We characterise representation…

We prove an algebraic version of the Gauge-Invariant Uniqueness Theorem, a result which gives information about the injectivity of certain homomorphisms between ${\mathbb Z}$-graded algebras. As our main application of this theorem, we…

We compute the monoid $V(L_K(E))$ of isomorphism classes of finitely generated projective modules over certain graph algebras $L_K(E)$, and we show that this monoid satisfies the refinement property and separative cancellation. We also show…

In this paper a bijection between the set of prime ideals of a Leavitt path algebra $L_K(E)$ and a certain set which involves maximal tails in $E$ and the prime spectrum of $K[x,x^{-1}]$ is established. Necessary and sufficient conditions…

Let $E$ be an arbitrary (countable) graph and let $R$ be a unital commutative ring. We analyze the ideal structure of the Leavitt path algebra $\lr$ introduced by Mark Tomforde. We first modify the definition of basic ideals and we then…

Let $L_K(E)$ denote the Leavitt path algebra associated to the finite graph $E$ and field $K$. For any closed path $c$ in $E$, we define and investigate the uniserial, artinian, non-noetherian left $L_K(E)$-module $U_{E,c-1}$. The unique…

There is a tight relation between the geometry of a directed graph and the algebraic structure of a Leavitt path algebra associated to it. In this note, we show a similar connection between the geometry of the graph and the structure of a…

A graph is called $(k,t)$-regular if it is $k$-regular and the induced subgraph on the neighbourhood of every vertex is $t$-regular. We find new conditions on $(k,t)$ for the existence of such graphs and provide a wide range of examples.

We prove Leavitt path algebra versions of the two uniqueness theorems of graph C*-algebras. We use these uniqueness theorems to analyze the ideal structure of Leavitt path algebras and give necessary and sufficient conditions for their…