A unified approach to Exel-Laca algebras and C*-algebras associated to graphs
By M. Tomforde. 2001
95 citations recorded by the source corpus.
We define an ultragraph, which is a generalization of a directed graph, and describe how to associate a C*-algebra to it. We show that the class of ultragraph algebras contains the C*-algebras of graphs as well as the Exel-Laca algebras. We also show that many of the techniques used for graph algebras can be applied to ultragraph algebras and that the ultragraph provides a useful tool for analyzing Exel-Laca algebras. Our results include versions of the Cuntz-Krieger Uniqueness Theorem and the Gauge-Invariant Uniqueness Theorem for ultragraph algebras.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1956bc0078cbd055438e3bdd66c1d20cd7be613c
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In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- Infinite alphabet edge shift spaces via ultragraphs and their C*-algebras (2017, methodology): “The associated C*-algebras form a class that strictly contain graph C*-algebras and the Exel-Laca algebras, see [29, 30].”
- Dynamical systems associated to separated graphs, graph algebras, and paradoxical decompositions☆ (2012, background): “Since then, there has been a long and fruitful interaction between the theory of combinatorially defined C*-algebras and dynamics, see [21], [40], [39], [26], [38], [12], [29], [11], [46], [55], [50], [49], [48], [28], [25].”
- Flow equivalence of graph algebras (2002, methodology): “It follows that the boundary @T of T is homeomorphic to the boundary @T 0 of T 0 (see [KP, x4]).”
- Inverse semigroups and combinatorial C*-algebras (2007, unknown): “Mathematical subject classification: Primary: 46L05; Secondary: 18B40.”
- Simplicity of ultragraph algebras (2001, background): “O A ] 5 A ug 2”