Removing Sources from Higher-rank Graphs
نویسنده
چکیده
For a higher-rank graph Λ with sources we detail a construction that creates a row-finite higher-rank graph Λ that does not have sources and contains Λ as a subgraph. Furthermore, when Λ is row-finite the Cuntz-Krieger algebra of Λ, C(Λ) is a full corner of C(Λ), the Cuntz-Krieger algebra of Λ.
منابع مشابه
Simplicity of C-algebras Associated to Row-finite Locally Convex Higher-rank Graphs
In previous work, the authors showed that the C∗-algebra C∗(Λ) of a rowfinite higher-rank graph Λ with no sources is simple if and only if Λ is both cofinal and aperiodic. In this paper, we generalise this result to row-finite higher-rank graphs which are locally convex (but may contain sources). Our main tool is Farthing’s “removing sources” construction which embeds a row-finite locally conve...
متن کاملTopological spaces associated to higher-rank graphs
We investigate which topological spaces can be constructed as topological realisations of higher-rank graphs. We describe equivalence relations on higher-rank graphs for which the quotient is again a higher-rank graph, and show that identifying isomorphic co-hereditary subgraphs in a disjoint union of two rank-k graphs gives rise to pullbacks of the associated C∗algebras. We describe a combinat...
متن کاملReal Rank and Topological Dimension of Higher Rank Graph Algebras
We study dimension theory for the C∗-algebras of row-finite k-graphs with no sources. We establish that strong aperiodicity—the higher-rank analogue of condition (K)—for a k-graph is necessary and sufficient for the associated C∗-algebra to have topological dimension zero. We prove that a purely infinite 2-graph algebra has real-rank zero if and only if it has topological dimension zero and sat...
متن کاملThe 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...
متن کاملA Dual Graph Construction for Higher-rank Graphs, and K-theory for Finite 2-graphs
Given a k-graph Λ and an element p of N, we define the dual k-graph, pΛ. We show that when Λ is row-finite and has no sources, the C∗-algebras C∗(Λ) and C∗(pΛ) coincide. We use this isomorphism to apply Robertson and Steger’s results to calculate the K-theory of C∗(Λ) when Λ is finite and strongly connected and satisfies the aperiodicity condition.
متن کامل