Cohn Path Algebras of Higher-Rank Graphs

@article{Clark2016CohnPA,
  title={Cohn Path Algebras of Higher-Rank Graphs},
  author={Lisa Orloff Clark and Yosafat E. P. Pangalela},
  journal={Algebras and Representation Theory},
  year={2016},
  volume={20},
  pages={47-70}
}
In this article, we introduce Cohn path algebras of higher-rank graphs. We prove that for a higher-rank graph Λ, there exists a higher-rank graph T Λ such that the Cohn path algebra of Λ is isomorphic to the Kumjian-Pask algebra of T Λ. We then use this isomorphism and properties of Kumjian-Pask algebras to study Cohn path algebras. This includes proving a uniqueness theorem for Cohn path algebras. 
Analogues of Leavitt path algebras for higher-rank graphs
Directed graphs and their higher-rank analogues provide an intuitive framework to study a class of C∗-algebras which we call graph algebras. The theory of graph algebras has been developed by aExpand
The Groupoid Approach to Leavitt Path Algebras
When the theory of Leavitt path algebras was already quite advanced, it was discovered that some of the more difficult questions were susceptible to a new approach using topological groupoids. TheExpand

References

SHOWING 1-10 OF 44 REFERENCES
The C*-algebras of finitely aligned higher-rank graphs
We generalise the theory of Cuntz–Krieger families and graph algebras to the class of finitely aligned k-graphs. This class contains in particular all row-finite k-graphs. The Cuntz–Krieger relationsExpand
Kumjian-Pask algebras of finitely-aligned higher-rank graphs
We extend the the definition of Kumjian-Pask algebras to include algebras associated to finitely aligned higher-rank graphs. We show that these Kumjian-Pask algebras are universally defined and haveExpand
Kumjian-Pask algebras of higher-rank graphs
We introduce higher-rank analogues of the Leavitt path algebras, which we call the Kumjian-Pask algebras. We prove graded and Cuntz-Krieger uniqueness theorems for these algebras, and analyze theirExpand
HIGHER-RANK GRAPHS AND THEIR $C^*$-ALGEBRAS
Abstract We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz–Krieger algebras. We describe a variant of the Cuntz–Krieger relations which applies toExpand
Realising the Toeplitz algebra of a higher-rank graph as a Cuntz-Krieger algebra
For a row-finite higher-rank graph �, we construct a higher-rank graph T� such that the Toeplitz algebra ofis isomorphic to the Cuntz-Krieger algebra of T�. We then prove that the higher-rank graphExpand
Higher Rank Graph C-Algebras
Building on recent work of Robertson and Steger, we associate a C{algebra to a combinatorial object which may be thought of as a higher rank graph. This C{algebra is shown to be isomorphic to that ofExpand
Groupoid models for the C*-algebras of topological higher-rank graphs
We provide groupoid models for Toeplitz and Cuntz-Krieger algebras of topological higher-rank graphs. Extending the groupoid models used in the theory of graph algebras and topological dynamicalExpand
Higher-Rank Graph C *-Algebras: An Inverse Semigroup and Groupoid Approach
AbstractWe provide inverse semigroup and groupoid models for the Toeplitz and Cuntz-Krieger algebras of finitely aligned higher-rank graphs. Using these models, we prove a uniqueness theorem for theExpand
Kumjian-Pask algebras of locally convex higher-rank graphs
The Kumjian-Pask algebra of a higher-rank graph generalises the Leavitt path algebra of a directed graph. We extend the definition of Kumjian-Pask algebra to row-finite higher-rank graphs $\Lambda$Expand
Simplicity of C*‐algebras associated to higher‐rank graphs
We prove that ifis a row-finite k-graph with no sources, then the associated C � -algebra is simple if and only ifis cofinal and satisfies Kumjian and Pask's aperiodicity condition, known asExpand
...
1
2
3
4
5
...