Related papers: The Algebraic Kirchberg-Phillips Question for Leav…

Suppose that $R$ is an associative unital ring and that $E=(E^0,E^1,r,s)$ is a directed graph. Utilizing results from graded ring theory we show, that the associated Leavitt path algebra $L_R(E)$ is simple if and only if $R$ is simple,…

We show that the K-theory cosheaf is a complete invariant for separable continuous fields with vanishing boundary maps over a finite-dimensional compact metrizable topological space whose fibers are stable Kirchberg algebras with rational…

Let A be a separable unital nuclear purely infinite simple C*-algebra satisfying the Universal Coefficient Theorem, and such that the K_0-class of the identity is zero. We prove that every automorphism of order two of the K-theory of A is…

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…

In sharp contrast to the Abrams-Rangaswamy Theorem that the only von Neumann regular Leavitt path algebras are exactly those associated to acyclic graphs, here we prove that the Leavitt path algebra of any arbitrary graph is a graded von…

This paper lays out the foundations of graded $K$-theory for Leavitt algebras associated with higher-rank graphs, also known as Kumjian-Pask algebras, establishing it as a potential tool for their classification. For a row-finite $k$-graph…

In this paper we completely describe graphically Leavitt path algebras with bounded index of nilpotence. We show that the Leavitt path algebra $L_{K}(E)$ has index of nilpotence at most $n$ if and only if no cycle in the graph $E$ has an…

We show that the graded Grothendieck group classifies unital Leavitt path algebras of primitive graphs up to graded homotopy equivalence. To this end, we further develop classification techniques for Leavitt path algebras by means of…

We show that certain pullbacks of $*$-algebras equivariant with respect to a compact group action remain pullbacks upon completing to $C^*$-algebras. This unifies a number of results in the literature on graph algebras, showing that…

Starting from Kirchberg's theorems announced in 1994, namely O_2 tensor A is isomorphic to O_2 for separable unital nuclear simple A and O_infinity tensor A is isomorphic to A if in addition A is purely infinite, we prove that…

Given an arbitrary graph, we describe the center of its Leavitt path algebra over a commutative unital ring. Our proof uses the Steinberg algebra model of the Leavitt path algebra. A key ingredient is a characterization of compact open…

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…

We describe how boundary paths in a graph can be used to construct irreducible representations of the associated graph C*-algebra and the associated Leavitt path algebra. We use this construction to establish two sets of results: First, we…

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…

We give the necessary and sufficient condition for a separated Cohn-Leavitt path algebra of a finite digraph to have IBN. As a consequence, separated Cohn path algebras have IBN. We determine the non-stable K-theory of a corner ring in…

In this paper, we classify all Leavitt path algebras which have the property that every Lie ideal is an ideal. As an application, we show that Leavitt path algebras with this property provide a class of locally finite, infinite-dimensional…

We consider a method popular in the literature of associating a two-step nilpotent Lie algebra with a finite simple graph. We prove that the two-step nilpotent Lie algebras associated with two graphs are Lie isomorphic if and only if the…

We show that separable continuous fields over the unit interval whose fibers are stable Kirchberg algebras that satisfy the universal coefficient theorem in KK-theory and have rational K-theory groups are classified up to isomorphism by…

We show that if a field k contains sufficiently many elements(for instance, if k is infinite), and K is an algebraically closed field containing k, then every linear algebraic k-group over K is k-isomorphic to Aut(A\otimes_kK), where A is a…