Related papers: The classification question for Leavitt path algeb…
We introduce a class of topologies on the Leavitt path algebra $L(\Gamma)$ of a finite directed graph and decompose a graded completion $\widehat{L}(\Gamma)$ as a direct sum of minimal ideals.
In this paper, we study ideal- and congruence-simpleness for the Leavitt path algebras of directed graphs with coefficients in a commutative semiring S, as well as establish some fundamental properties of those algebras. We provide a…
In the thesis we present a new method for parametrizing algebraic varieties over the field of characteristic zero. The problem of parametrizing is reduced to a problem of finding an isomorphism of algebras. We introduce the Lie algebra of a…
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…
Leavitt path algebras of bi-separated graphs have been recently introduced by R. Mohan and B. Suhas. These algebras provide a common framework for studying various generalisations of Leavitt path algebras. In this paper we obtain modules…
In this paper we study the algebra of graph invariants, focusing mainly on the invariants of simple graphs. All other invariants, such as sorted eigenvalues, degree sequences and canonical permutations, belong to this algebra. In fact,…
We investigate the algebra of a Hausdorff ample groupoid, introduced by Steinberg, over a commutative semiring S. In particular, we obtain a complete characterization of congruence-simpleness for such Steinberg algebras, extending the…
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…
The paper aims to investigate the classification problem of low dimensional complex none Lie filiform Leibniz algebras. There are two sources to get classification of filiform Leibniz algebras. The first of them is the naturally graded none…
We study relative Cohn path algebras, also known as Leavitt-Cohn path algebras, and we realize them as partial skew group rings (to do this we prove uniqueness theorems for relative Cohn path algebras). Furthermore, given any graph $E$ we…
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…
For any field $K$ and for a completely arbitrary graph $E$, we characterize the Leavitt path algebras $L_K(E)$ that are indecomposable (as a direct sum of two-sided ideals) in terms of the underlying graph. When the algebra decomposes, it…
It is a conjecture that for the class of Leavitt path algebras associated to finite directed graphs, their graded Grothendieck groups $K_0^{\mathrm{gr}}$ are a complete invariant. For a Leavitt path algebra $L_{\mathsf k}(E)$, with…
We study Steinberg algebras constructed from ample Hausdorff groupoids over commutative integral domains with identity. We reconstruct (graded) groupoids from (graded) Steinberg algebras and use this to characterise when there is a…
The construction of the Leavitt path algebra associated to a directed graph $E$ is extended to incorporate a family $C$ consisting of partitions of the sets of edges emanating from the vertices of $E$. The new algebras, $L_K(E,C)$, are…
It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…
A ring R is called right principally-injective if every R-homomorphism from a principal right ideal aR to R (a in R), extends to R, or equivalently if every system of equations xa=b (a, b in R) is solvable in R. In this paper we show that…
In this note we prove that the algebras $L_K(E)$ and $KE$ have the same entropy. Entropy is always referred to the standard filtrations in the corresponding kind of algebra. The main argument leans on (1) the holomorphic functional…
We develop a technique to show the Morita equivalence of certain subrings of a ring with local units. We then apply this technique to develop conditions that are sufficient to show the Morita equivalence of subalgebras induced by partial…
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…