Related papers: The Leavitt path algebra of a graph

We study path rings, Cohn path rings, and Leavitt path rings associated to directed graphs, with coefficients in an arbitrary ring $R$. For each of these types of rings, we stipulate conditions on the graph that are necessary and sufficient…

Let $E$ be an arbitrary directed graph and let $L$ be the Leavitt path algebra of the graph $E$ over a field $K$. It is shown that every ideal of $L$ is an intersection of primitive/prime ideals in $L$ if and only if the graph $E$ satisfies…

In this paper, the quotient of a Leavitt path algebra of an arbitrary graph by an $I$-basic graded ideal, and the quotient of a Leavitt path algebra of a row-finite graph by an arbitrary graded ideal are considered. The result of the…

We provide a characterization of graded von Neumann regular rings involving the recently introduced class of nearly epsilon-strongly graded rings. As our main application, we generalize Hazrat's result that Leavitt path algebras over fields…

We investigate conditions under which the endomorphism ring of the Leavitt path algebra $L_{K}(E)$ possesses various ring and module-theoretical properties such as being von Neumann regular, $\pi$-regular, strongly $\pi$-regular or…

We relate two conjectures which have been raised for classification of Leavitt path algebras. For purely infinite simple unital Leavitt path algebras, it is conjectured that K_0 classifies them completely. For arbitrary Leavitt path…

We study the center of several types of path algebras. We start with the path algebra $KE$ and prove that if the number of vertices is infinite then the center is zero. Otherwise, it coincides with the field $K$ except when the graph $E$ is…

Let $n$ be a positive integer. For each $0\leq j \leq n-1$ we let $C_n^j$ denote the Cayley graph of the cyclic group $\mathbb{Z}_n$ with respect to the subset $\{1,j\}$. Utilizing the Smith Normal Form process, we give an explicit…

We introduce filtered algebraic $K$-theory of a ring $R$ relative to a sublattice of ideals. This is done in such a way that filtered algebraic $K$-theory of a Leavitt path algebra relative to the graded ideals is parallel to the gauge…

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)…

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.…

This paper is an attempt to show that, parallel to Elliott's classification of AF $C^*$-algebras by means of $K$-theory, the graded $K_0$-group classifies Leavitt path algebras completely. In this direction, we prove this claim at two…

Let $K$ be a field, let $E$ be a finite directed graph, and let $L_K(E)$ be the Leavitt path algebra of $E$ over $K$. We show that for a prime ideal $P$ in $L_K(E)$, the following are equivalent: \begin{enumerate} \item $P$ is primitive;…

We establish necessary and sufficient conditions on a (not necessarily countable) graph E for the graph C*-algebra C*(E) to be primitive. Along with a known characterization of the graphs E for which C*(E) is prime, our main result provides…

We characterize Leavitt path algebras which are Rickart, Baer, and Baer $*$-rings in terms of the properties of the underlying graph. In order to treat non-unital Leavitt path algebras as well, we generalize these annihilator-related…

The primary purpose of this thesis is to show every ultragraph Leavitt path algebra is Morita equivalent, as a ring, to a graph Leavitt path algebra. Takeshi Katsura, Paul Muhly, Aidan Sims, and Mark Tomforde showed every ultragraph…

Let $\xi:C^*(E)\to C^*(F)$ be a unital $*$-homomorphism between simple purely infinite Cuntz-Krieger algebras of finite graphs. We prove that there exists a unital $*$-homomorphism $\phi:L(E)\to L(F)$ between the corresponding Leavitt…

If $E$ is a not-necessarily row-finite graph, such that each vertex of $E$ emits at most countably many edges, then a {\it desingularization} $F$ of $E$ can be constructed (see e.g. (1) G. Abrams, G. Aranda Pino, Leavitt path algebras of…

In this article, we describe the endomorphism ring of a finitely generated progenerator module of a weighted Leavitt path algebra $L_{K}(E, w)$ of a finite vertex weighted graph $(E, w)$. Contrary to the case of Leavitt path algebras, we…

We show that the graph construction used to prove that a gauge-invariant ideal of a graph C*-algebra is isomorphic to a graph C*-algebra, and also used to prove that a graded ideal of a Leavitt path algebra is isomorphic to a Leavitt path…