The Leavitt path algebras of arbitrary graphs

By G. Abrams, G. Pino. 2008

126 citations recorded by the source corpus.

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Citations in the corpus

Irreducible representations of Leavitt path algebras (2011, methodology): “ basic notions related to quivers and Leavitt path algebras, and introduce some terminologies for later use. The references for quivers are [5, Chapter III] and [1], and for Leavitt path algebras are [1, 2, 6]. 2.1. Quivers and left-inﬁnite paths. Recall that a quiver Q= (Q 0,Q 1;s,t) consists of a ”
Socle theory for Leavitt path algebras of arbitrary graphs (2008, background): “-ﬁnite graph F, called a desingularization of E, such that LK(E) is Morita equivalent to LK(F) as rings with local units [3, Theorem 5.2]. The process of building the graph F out of E is described in [18, 3] and it essentially consists, as the name suggests, on conveniently removing the singular ver”
Leavitt Path Algebras as Partial Skew Group Rings (2012, methodology): “The following result appeared first in [2] (lemma 2.”
The Theory of Prime Ideals of Leavitt Path Algebras over Arbitrary Graphs (2011, background): “1 of [2] and so there are non-zero ideals in LK(E).”
Leavitt path algebras with coefficients in a commutative ring (2009, background): “(The definition in [1] was given for row-finite directed graphs, but the authors later extended the definition in [2] to all directed graphs.”
The complete classification of unital graph C∗-algebras: Geometric and strong (2016, background): “ in [AT11] that if the Leavitt path algebrasLC(E) and LC(F) are Moritaequivalent, respectively isomorphic as rings, then C∗(E) and C∗(F) are strongly Morita equivalent, respectively ∗-isomorphic (see [AAP08] for the deﬁnition of LC(E)). Since the formulation of the conjectures in 2011, it has been c”
Simplicity, primitivity and semiprimitivity of etale groupoid algebras with applications to inverse semigroup algebras (2014, methodology): “We also note that the semiprimitivity of Leavitt path algebras over any base field [1] is an immediate consequence of our results.”
Leavitt path algebras: the first decade (2014, methodology): “It is shown in [9] that the Leavitt path algebra of any such countable graph is Morita equivalent to the Leavitt path algebra of a suitably defined row-finite graph, using the desingularization process.”
Analogs of Cuntz algebras on Lp spaces (2012, methodology): “sary to distinguish the generators of L∞ from those of Ld and Cd, we denote them by s(∞) 1 ,s (∞) 2 ,...,t (∞) 1 ,t (∞) 2 ,.... 4 N. CHRISTOPHER PHILLIPS This algebra is simple, by Example 3.1(ii) of [3]. Remark 1.4. The algebras Ld, Cd, and L∞ are all examples of Leavitt path algebras. For Ld see E”