Related papers: Leavitt path algebras satisfying a polynomial iden…

Leavitt path algebras associate to directed graphs a $\mathbb Z$-graded algebra and in their simplest form recover the Leavitt algebras $L(1,k)$. In this note, we first study this $\mathbb Z$-grading and characterize the ($\mathbb…

We show that every subset of vertices of a directed graph E gives a Morita equivalence between a subalgebra and an ideal of the associated Leavitt path algebra. We use this observation to prove an algebraic version of a theorem of Crisp and…

In this paper, using pseudo path algebras, we generalize Gabriel's Theorem on elementary algebras to left Artinian algebras over a field $k$ when it is splitting over its radical, in particular, when the dimension of the quotient algebra…

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…

The graph groupoids of directed graphs are topologically isomorphic if and only if there is a diagonal-preserving ring *-isomorphism between the Leavitt path algebras.

We construct a nil algebra over a countable field which has finite but non-zero Gelfand-Kirillov dimension.

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…

Leavitt path algebras are free algebras subject to relations induced by directed graphs. This paper investigates the ideals of Leavitt path algebras, with an emphasis on the relationship between graph-theoretic properties of a directed…

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;…

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…

It is shown that the Hecke-Kiselman algebra associated to a finite directed graph is an automaton algebra in the sense of Ufnarovskii. Consequently, its Gelfand-Kirillov dimension is an integer if it is finite. As a consequence, it is…

Between the braided vector spaces of diagonal type there exist some families whose associated Nichols algebras are infinite dimensional but with finite Gelfand-Kirillov dimension, called one-parameter families. We show that every…

We prove that to every inclusion $A\hookrightarrow L$ of Lie algebroids over the same base manifold $M$ corresponds a Kapranov dg-manifold structure on $A[1]\oplus L/A$, which is canonical up to isomorphism. As a consequence,…

Let $G$ be a group and $\ell$ a commutative unital $\ast$-ring with an element $\lambda \in \ell$ such that $\lambda + \lambda^\ast = 1$. We introduce variants of hermitian bivariant $K$-theory for $\ast$-algebras equipped with a $G$-action…

Graph polynomials are deemed useful if they give rise to algebraic characterizations of various graph properties, and their evaluations encode many other graph invariants. Algebraic: The complete graphs $K_n$ and the complete bipartite…

We investigate polynomial endomorphisms of graph $C^*$-algebras and Leavitt path algebras. To this end, we define and analyze the coding graph corresponding to each such an endomorphism. We find an if and only if condition for the…

This article sets out to understand the categories $\QGr A$ where $A$ is either a monomial algebra or a path algebra of finite Gelfand-Kirillov dimension. The principle questions are: 1) What is the structure of the point modules up to…

Given a simple undirected graph, one can construct from it a $c$-step nilpotent Lie algebra for every $c \geq 2$ and over any field $K$, in particular also over the real and complex numbers. These Lie algebras form an important class of…

We prove that the C*-algebra of a directed graph $E$ is liminal iff the graph satisfies the finiteness condition: if $p$ is an infinite path or a path ending with a sink or an infinite emitter, and if $v$ is any vertex, then there are only…

In this article, we give a new class of automorphisms of Leavitt path algebras of arbitrary graphs. Consequently, we obtain Anick type automorphisms of these Leavitt path algebras and new irreducible representations of Leavitt algebras of…