Related papers: The graded structure of Leavittt path algebras vie…

We obtain a complete structural characterization of Cohn-Leavitt algebras over no-exit objects as graded involutive algebras. Corollaries of this result include graph-theoretic conditions characterizing when a Leavitt path algebra is a…

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…

In this paper we show that Leavitt path algebras of weighted graphs and Leavitt path algebras of separated graphs are intimately related. We prove that any Leavitt path algebra $L(E,\omega)$ of a row-finite vertex weighted graph…

For any field K and directed graph E, we completely describe the elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E),L_K(E)]. We then use this result to classify all Leavitt path algebras L_K(E) that…

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…

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…

Motivated by recent results in graph C*-algebras concerning an equivariant pushout structure of the Vaksman-Soibelman quantum odd spheres, we introduce a class of graphs called trimmable. Then we show that the Leavitt path algebra of a…

We show how to reconstruct a graded ample Hausdorff groupoid with topologically principal neutrally graded component from the ring structure of its graded Steinberg algebra over any commutative integral domain with 1, together with the…

We determine the Gelfand-Kirillov dimension of a weighted Leavitt path algebra $L_K(E,w)$ where $K$ is a field and $(E,w)$ a finite weighted graph. Further we show that a finite-dimensional weighted Leavitt path algebra over a field $K$ is…

We define Leavitt path algebras of hypergraphs generalizing simultaneously Leavitt path algebras of finitely separated graphs and Leavitt path algebras of row-finite vertex-weighted graphs. We find linear bases for those algebras, compute…

The Graded Classification Conjecture states that for finite directed graphs $E$ and $F$, the associated Leavitt path algebras $L_\K(E)$ and $L_\K(F)$ are graded Morita equivalent, i.e., $\Gr L_\K(E) \approx_{\gr} \Gr L_\K(F)$, if and only…

Let $E$ be a finite directed graph, and let $I$ be the poset obtained as the antisymmetrization of its set of vertices with respect to a pre-order $\le$ that satisfies $v\le w$ whenever there exists a directed path from $w$ to $v$. Assuming…

In this article we generalize a classical result by Passman on primeness of unital strongly group graded rings to the class of nearly epsilon-strongly group graded rings which are not necessarily unital. Using this result, we obtain (i) a…

Hazrat gave a K-theoretic invariant for Leavitt path algebras as graded algebras. Hazrat conjectured that this invariant classifies Leavitt path algebras up to graded isomorphism, and proved the conjecture in some cases. In this paper, we…

We show that if $E$ is an arbitrary acyclic graph then the Leavitt path algebra $L_K(E)$ is locally $K$-matricial; that is, $L_K(E)$ is the direct union of subalgebras, each isomorphic to a finite direct sum of finite matrix rings over the…

Let $E$ be a directed graph, $K$ any field, and let $L_K(E)$ denote the Leavitt path algebra of $E$ with coefficients in $K$. We show that $L_K(E)$ is a B\'{e}zout ring, i.e., that every finitely generated one-sided ideal of $L_K(E)$ is…

We prove that a unital shift equivalence induces a graded isomorphism of Leavitt path algebras when the shift equivalence satisfies an alignment condition. This yields another step towards confirming the Graded Classification Conjecture.…

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 associate in a natural way to any partially ordered set $(P,\leq)$ a directed graph $E_P$ (where the vertices of $E_P$ correspond to the elements of $P$, and the edges of $E_P$ correspond to related pairs of elements of $P$), and then…

Let $K$ be a field and $E$ be a graph. Let $L_K(E)$ be the Leavitt path algebra of $E$ over $K$ with the standard involution $^\star$. We investigate the set of skew-symmetric elements, $\mathbf{K}_{L_K(E)}=\{x\in L_K(E) : x^{\star}=-x\}$,…