Leavitt path algebras: the first decade
G Abrams - Bulletin of Mathematical Sciences, 2015 - Springer
The algebraic structures known as Leavitt path algebras were initially developed in 2004 by
Ara, Moreno and Pardo, and almost simultaneously (using a different approach) by the …
Ara, Moreno and Pardo, and almost simultaneously (using a different approach) by the …
Graded Steinberg algebras and their representations
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 …
ample Hausdorff groupoid. In the first part of the paper, we show that this category is …
Graded irreducible representations of Leavitt path algebras: A new type and complete classification
L Vaš - Journal of Pure and Applied Algebra, 2023 - Elsevier
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 …
class is new in the sense that its representation space is not isomorphic to any of the existing …
[HTML][HTML] Extensions of simple modules over Leavitt path algebras
Let E be a directed graph, K any field, and let LK (E) denote the Leavitt path algebra of E
with coefficients in K. For each rational infinite path c∞ of E we explicitly construct a …
with coefficients in K. For each rational infinite path c∞ of E we explicitly construct a …
[HTML][HTML] On graded irreducible representations of Leavitt path algebras
R Hazrat, KM Rangaswamy - Journal of Algebra, 2016 - Elsevier
Using the E-algebraic branching systems, various graded irreducible representations of a
Leavitt path K-algebra L of a directed graph E are constructed. The concept of a Laurent …
Leavitt path K-algebra L of a directed graph E are constructed. The concept of a Laurent …
[HTML][HTML] On simple modules over Leavitt path algebras
KM Rangaswamy - Journal of Algebra, 2015 - Elsevier
Given an arbitrary graph E and any field K, a new class of simple modules over the Leavitt
path algebra LK (E) is constructed by using vertices that emit infinitely many edges in E. The …
path algebra LK (E) is constructed by using vertices that emit infinitely many edges in E. The …
[HTML][HTML] Special irreducible representations of Leavitt path algebras
PN Ánh, TG Nam - Advances in Mathematics, 2021 - Elsevier
Several descriptions of irreducible representations of both Leavitt and hence Cohn path
algebras of an arbitrary digraph with coefficients in a commutative field introduced by Chen …
algebras of an arbitrary digraph with coefficients in a commutative field introduced by Chen …
Graphs with disjoint cycles classification via the talented monoid
We characterise directed graphs consisting of disjoint cycles via their talented monoids. We
show that a graph E consists of disjoint cycles precisely when its talented monoid TE has a …
show that a graph E consists of disjoint cycles precisely when its talented monoid TE has a …
Finite-dimensional representations of Leavitt path algebras
A Koç, M Özaydın - Forum Mathematicum, 2018 - degruyter.com
When Γ is a row-finite digraph, we classify all finite-dimensional modules of the Leavitt path
algebra L(Γ) via an explicit Morita equivalence given by an effective combinatorial …
algebra L(Γ) via an explicit Morita equivalence given by an effective combinatorial …
[HTML][HTML] Representations of Leavitt path algebras
A Koç, M Özaydın - Journal of pure and applied algebra, 2020 - Elsevier
We study representations of a Leavitt path algebra L of a finitely separated digraph Γ over a
field. We show that the category of L-modules is equivalent to a full subcategory of quiver …
field. We show that the category of L-modules is equivalent to a full subcategory of quiver …