منابع مشابه
The path space of a higher-rank graph
We construct a locally compact Hausdorff topology on the path space of a finitely aligned k -graph Λ . We identify the boundary-path space ∂Λ as the spectrum of a commutative C ∗ -subalgebra D Λ of C ∗ (Λ) . Then, using a construction similar to that of Farthing, we construct a finitely aligned k -graph Λ ̃ with no sources in which Λ is embedded, and show that ∂Λ is homeomorphic to a subset of ...
متن کاملHigher Rank Graph Algebras
These are lecture notes of a course given by Alex Kumjian at the RMMC Summer School at the University of Wyoming, Laramie, June 1-5, 2015. Warning: little proofreading has been done.
متن کاملThe Path Space of a Directed Graph
We construct a locally compact Hausdorff topology on the path space of a directed graph E and identify its boundary-path space ∂E as the spectrum of a commutative C∗-subalgebra DE of C∗(E). We then show that ∂E is homeomorphic to a subset of the infinite-path space of any desingularisation F of E. Drinen and Tomforde showed that we can realise C∗(E) as a full corner of C∗(F ), and we deduce tha...
متن کاملHigher 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 of the associated path groupoid. Various results in this paper give sufficient conditions on the higher rank graph for the associated C∗–algebra to be: simple, purely infinite and AF. Results concer...
متن کاملRepresentations of higher rank graph algebras
Let F+θ be a k-graph on a single vertex. We show that every irreducible atomic ∗-representation is the minimal ∗-dilation of a group construction representation. It follows that every atomic representation decomposes as a direct sum or integral of such representations. We characterize periodicity of F+θ and identify a symmetry subgroup Hθ of Z. If this has rank s, then C(Fθ ) ∼= C(T) ⊗ A for so...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2011
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm204-2-4