Related papers: Free path groupoid grading on Leavitt path algebra…

For any row-finite graph $E$ and any field $K$ we construct the {\its Leavitt path algebra} $L(E)$ having coefficients in $K$. When $K$ is the field of complex numbers, then $L(E)$ is the algebraic analog of the Cuntz Krieger algebra…

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 characterize ultragraph Leavitt path algebras that are Rickart, locally Rickart, graded Rickart, and graded Rickart *-rings. We also characterize ultragraph Leavitt path algebras that are Baer, locally Baer, graded Baer, Baer *-rings,…

Let $R$ be an algebra over a commutative ring $k$. Suppose that $R$ is endowed with a descending filtration indexed on an ordered group $(G,<)$ such that the restriction to $k$ is positive. We show that the existence of free algebras on a…

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 provide a complete answer to the question "When is a quotient of a Leavitt path algebra isomorphic to a Leavitt path algebra?" in terms of the interaction of the kernel of the quotient homomorphism with the cycles of the digraph. A key…

We present a new class of graded irreducible representations of a Leavitt path algebra. This class is new in the sense that its representation space is not isomorphic to any of the existing simple Chen modules. The corresponding graded…

We study the category of left unital graded modules over the Steinberg algebra of a graded ample Hausdorff groupoid. In the first part of the paper, we show that this category is isomorphic to the category of unital left modules over the…

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…

We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…

For any positive integer $n$ we describe the Leavitt path algebra of the Cayley graph $C_n$ corresponding to the cyclic group $\Z/n\Z$. Using a Kirchberg-Phillips-type realization result, we show that there are exactly four isomorphism…

Leavitt path algebras are shown to be algebras of right quotients of their corresponding path algebras. Using this fact we obtain maximal algebras of right quotients from those (Leavitt) path algebras whose associated graph satisfies that…

Given a directed graph E we describe a method for constructing a Leavitt path algebra $L_R(E)$ whose coefficients are in a commutative unital ring R. We prove versions of the Graded Uniqueness Theorem and Cuntz-Krieger Uniqueness Theorem…

We investigate the group gradings on the algebra of upper triangular matrices over an arbitrary field, viewed as a Lie algebra. These results were obtained a few years early by the same authors. We provide streamlined proofs, and present a…

Using the E-algebraic systems, various graded irreducible representations of a Leavitt path algebra L of a graph E over a field K are constructed. The concept of a Laurent vertex is introduced and it is shown that the minimal graded left…

We prove that an isomorphism of graded Grothendieck groups $K^{gr}_0$ of two Leavitt path algebras induces an isomorphism of a certain quotient of algebraic filtered $K$-theory and consequently an isomorphism of filtered $K$-theory of their…

A $G$-grading on an algebra is called multiplicity free if each homogeneous component of the grading is 1-dimensional, where $G$ is an abelian group. We introduce skew root systems of Lie type and skew root systems of Jordan type…

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…

Weighted Leavitt path algebras (wLpas) are a generalisation of Leavitt path algebras (with graphs of weight 1) and cover the algebras $L_K(n, n + k)$ constructed by Leavitt. Using Bergman's Diamond lemma, we give normal forms for elements…

We achieve an extremely useful description (up to isomorphism) of the Leavitt path algebra $L_K(E)$ of a finite graph $E$ with coefficients in a field $K$ as a direct sum of matrix rings over $K$, direct sum with a corner of the Leavitt…