THE C -ALGEBRAS OF ROW-FINITE GRAPHS

By T. Bates, David Pask, Iain Raeburn. 2000

317 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b31ee93bbb511568ab025745b78bc432638ed5c4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. G. Abrams
2. G. Pino
3. P. Ara
4. M. Tomforde
5. Aidan Sims
6. Trent Yeend
7. R. Exel
8. Mercedes Siles Molina

Citations in the corpus

• Inverse semigroups and combinatorial C*-algebras (2007, unknown): “Mathematical subject classification: Primary: 46L05; Secondary: 18B40.”
• A groupoid generalisation of Leavitt path algebras (2014, background): “Versions of these theorems have been established for many generalisations of Cuntz-Krieger algebras [6, 9, 11, 12, 13, 19, 20].”
• Socle theory for Leavitt path algebras of arbitrary graphs (2008, result): “This was first don e in the analytic setting (see [15, 27, 28] among others), while the seminal results on Leavitt path algebras of row finite graphs appeared in [1] and [9], so starting a flurry of ac tivity.”
• Topological Quivers (2003, background): “[5, 46, 4, 14]) and as we shall see, their generaliztions play an equally important role in the analysis of C∗-algebras associated to topological quivers.”
• Uniqueness theorems and ideal structure for Leavitt path algebras (2006, result): “This result is analogous to the Gauge-Invariant Uniqueness Theorem for graph C ∗ -algebras ([ 9, Theorem 2.1 ] and [10, Theorem 2.1]).”
• GRAPH INVERSE SEMIGROUPS, GROUPOIDS AND THEIR C -ALGEBRAS (2003, background): “Further, as is pointed out in [1], it is technically easy to reduce to the case where there are no sinks.”
• Quantum Spheres and Projective Spaces as Graph Algebras (2002, background): “Indeed, the K0 and K1 groups of C(L2) are isomorphic to the cokernel and kernel, respectively, of the map KL2 : Z → Z2 corresponding to the matrix [ 0 2 ]”
• Kumjian-Pask algebras of higher-rank graphs (2011, methodology): “For operator algebraists, there is a well-trodden path for studying new analogues of Cuntz-Krieger algebras, which was developed in [19] and [9], and which was followed in the first four chapters of [28], for example.”
• Gauge-Invariant Ideals in the C*-Algebras of Finitely Aligned Higher-Rank Graphs (2004, result): “9 of [4], though our methods are more akin to those of [1].”
• Adding tails to $C^*$-correspondences (2002, unknown): “{e:s(e)=v} ses ∗ e for all v ∈ E with 0 < |s−1(v)| < ∞ The graph algebra C∗(E) is the C∗-algebra generated by a universal CuntzKrieger E-family (see [14, 13, 2, 5, 1]).”
• Rank-two graphs whose C∗-algebras are direct limits of circle algebras (2005, unknown): “For n ∈ N, let cn := 1, let An := [an], let Bn = [1] and let Tn := [an].”
• Purely infinite simple Leavitt path algebras (2005, result): “This result provides the algebraic analog to the corresponding result for the Cuntz-Krieger C-algebra C(E) given in [7].”
• Higher Rank Graph C-Algebras (2000, methodology): “[ BPRS , aHR], see also [CK, RS2] where similar techniques are used to prove simplicity).”
• The noncommutative geometry of graph C*-algebras I: The index theorem (2005, background): “1 The C∗-algebras of Graphs For a more detailed introduction to graph C∗-algebras we refer the reader to [2,20] and the references therein.”
• Leavitt path algebras with coefficients in a commutative ring (2009, methodology): “In the past five years, methods similar to those in [8], [7], [15], [5], [6], and [9] have been used to analyze the ideal structure of Leavitt path algebras over fields.”
• Quantum lens spaces and graph algebras (2003, background): “At first we describe closed 2-sided ideals of C∗(E) invariant under the gauge action, as well as the corresponding quotients [5, 12, 16, 2, 1, 10].”