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On the Ideals of Ultragraph Leavitt Path Algebras
In this article, we provide an explicit description of a set of generators for any ideal of an ultragraph Leavitt path algebra. We provide several...
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Hereditary Saturated Subsets and the Invariant Basis Number Property of the Leavitt Path Algebra of Cartesian Products
AbstractIn this note, first, we describe the (minimal) hereditary saturated subsets of finite acyclic graphs and finite graphs whose cycles have no...
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Algebraic Entropy of Path Algebras and Leavitt Path Algebras of Finite Graphs
The Gelfand–Kirillov dimension is a well established quantity to classify the growth of infinite dimensional algebras. In this article we introduce...
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Realization for tensor products of Leavitt path algebras
For two given graphs, we construct an augmentation graph. We obtain an injective algebra homomorphism from the Leavitt path algebra of the...
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Leavitt Path Algebras in Which Every Lie Ideal is an Ideal and Applications
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...
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Modules for Leavitt Path Algebras via Extended Algebraic Branching Systems
For a graph E , we introduce the notion of an extended E -algebraic branching system, generalising the notion of an E -algebraic branching system...
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Classifying Leavitt path algebras up to involution preserving homotopy
We prove that the Bowen–Franks group classifies the Leavitt path algebras of purely infinite simple finite graphs over a regular supercoherent...
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Basic One-Sided Ideals of Leavitt Path Algebras over Commutative Rings
In this article, basic left (right) ideals of Leavitt Path Algebra over a commutative unital ring are studied. We give conditions under which a basic...
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Representations and the reduction theorem for ultragraph Leavitt path algebras
In this paper, we study representations of ultragraph Leavitt path algebras via branching systems and, using partial skew ring theory, prove the...
