Leavitt path algebras and direct limits
By K. Goodearl. 2007
88 citations recorded by the source corpus.
An introduction to Leavitt path algebras of arbitrary directed graphs is presented, and direct limit techniques are developed, with which many results that had previously been proved for countable graphs can be extended to uncountable ones. Such results include characterizations of simplicity, characterizations of the exchange property, and cancellation conditions for the K-theoretic monoid of equivalence classes of idempotent matrices.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1e877ad26e75449c93f84044c3cb2d6a78187033
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In Algebra and Number Theory
- G. Abrams
- Kulumani M. Rangaswamy
- Mercedes Siles Molina
- G. Pino
- P. Ara
- K. Goodearl
- M. Tomforde
- Cándido Martín González
In Mathematical Physics
- G. Abrams
- Kulumani M. Rangaswamy
- Mercedes Siles Molina
- G. Pino
- P. Ara
- K. Goodearl
- M. Tomforde
- Cándido Martín González
Citations in the corpus
- Socle theory for Leavitt path algebras of arbitrary graphs (2008, background): “vitt path algebra LK(E) of a graph E and the path algebra KE associated to the same graph are closely enough: LK(E) is an algebra of right quotients of KE (see [29]). Apart from the very recent paper [22], by K. R. Goodearl, where he has introduced Leavitt path algebras of uncountable directed graph”
- Leavitt path algebras: the first decade (2014, background): “Subsequently, the more general definition of Leavitt path algebras for countable graphs ([9]), and then truly arbitrary graphs ([66]), appeared in the literature.”
- The Theory of Prime Ideals of Leavitt Path Algebras over Arbitrary Graphs (2011, background): “Conversely, it is well-known (see [15], [22]) that Condition (K) on E implies that every ideal of LK(E) is graded.”
- Leavitt path algebras of separated graphs (2010, background): “Leavitt path algebras LK(E), natural algebraic versions of graph C -algebras, were introduced and studied firstly in [1] and [9] for row-finite graphs, and in [2] and [39] for general graphs; see also [4], [5], [10], [11], [26].”
- Graded Steinberg algebras and their representations (2017, unknown): “2009, §5.3]).”
- Regularity Conditions for Arbitrary Leavitt Path Algebras (2008, methodology): “For a more complete description and discussion, see e.g. [2] or [ 8 ].”