Finite-dimensional Leavitt path algebras

By G. Abrams, G. Pino, Mercedes Siles Molina. 2007

86 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1df245ff419352d013c0a5a0f82a3e7b7f582c91

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In Algebra and Number Theory

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Citations in the corpus

Regularity Conditions for Arbitrary Leavitt Path Algebras (2008, background): “r the ﬁeld K. Asa consequence we get our main result, in which we show that the following conditions are equivalent for an arbitrary graph E: (1) LK(E) is von Neumann regular. (2) LK(E) is π-regular. (3) E is acyclic. (4) LK(E) is locally K-matricial. (5) LK(E) is strongly π-regular. We conclude by ”
Uniqueness theorems and ideal structure for Leavitt path algebras (2006, result): “Abrams and Aranda-Pino established basic properties of these Leavitt path algebras, and soon after there was a flurry of activity as many other authors [2, 3, 4 , 5, 6, 7, 8] investigated their structure and found applications to various topics in algebra.”
Chain conditions for Leavitt path algebras (2009, background): “done in [4] for finite-dimensional Leavitt path algebras, and the work done in [8], where the socle of a Leavitt path algebra was described.”
Locally finite Leavitt path algebras (2008, methodology): “In [ 3 ] the authors completely determine the structure of the finite dimensional”
The socle of a Leavitt path algebra (2007, background): “Concretely, necessary and sufficient conditions on a graph E have been given so that the corresponding Leavitt path algebra LK(E) is simple [1], purely infinite simple [2], exchange [7], finite dimensional [3], and locally finite (equivalently noetherian) [4].”
Leavitt Path Algebras as Partial Skew Group Rings (2012, background): “) in terms of intrinsic properties of the underlying graph, (see [3, 4, 5, 19]), and studied their relations with other”
Socle theory for Leavitt path algebras of arbitrary graphs (2008, background): “In addition, several other ring properties were studied in the case of row-finite Leavitt path algebras, such as being exchange [10], finite dimensional [ 5 ], noetherian [6], semisimple [4] or having stable rank [10, 8]. It has been also shown that the Leavitt path algebraL K (E)of a graphEand the ”