Cohn Path Algebras of Higher-Rank Graphs
نویسندگان
چکیده
منابع مشابه
The H Algebras of Higher Rank Graphs
We begin the study of a new class of operator algebras that arise from higher rank graphs. Every higher rank graph generates a Fock space Hilbert space and creation operators which are partial isometries acting on the space. We call the weak operator topology closed algebra generated by these operators a higher rank semigroupoid algebra. A number of examples are discussed in detail, including t...
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We prove that if Λ is a row-finite k-graph with no sources, then the associated C∗-algebra is simple if and only if Λ is cofinal and satisfies Kumjian and Pask’s Condition (A). We prove that Condition (A) is equivalent to a suitably modified version of Robertson and Steger’s original nonperiodicity condition (H3) which in particular involves only finite paths. We also characterise both cofinali...
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We introduce a homology theory for k-graphs and explore its fundamental properties. We establish connections with algebraic topology by showing that the homology of a k-graph coincides with the homology of its topological realisation as described by Kaliszewski et al. We exhibit combinatorial versions of a number of standard topological constructions, and show that they are compatible, from a h...
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These are notes for a short lecture course on k-graph C∗-algebras to be delivered at the Summer School on C∗-algebras and their interplay with dynamics at the Sophus Lie Conference Centre in Nordfjordeid, Norway in June 2010. They are not even remotely comprehensive of the work that many authors have done on k-graphs, nor are all details even of the material covered included. In addition, there...
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ژورنال
عنوان ژورنال: Algebras and Representation Theory
سال: 2016
ISSN: 1386-923X,1572-9079
DOI: 10.1007/s10468-016-9631-6