Monic representations of finite higher-rank graphs
نویسندگان
چکیده
منابع مشابه
Higher Dimensional Representations of Graphs
Graphs are often used to model complex systems and to visualize relationships , and this often involves drawing a graph in the plane. For this, a variety of algorithms and mathematical tools have been used with varying success. We demonstrate why it is often more natural and more meaningful to view higher dimensional representations of graphs. We present some of the theory and problems associat...
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 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 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 کاملHigher rank Einstein solvmanifolds
In this paper we study the structure of standard Einstein solvmanifolds of arbitrary rank. Also the validity of a variational method for finding standard Einstein solvmanifolds is proved.
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: Ergodic Theory and Dynamical Systems
سال: 2018
ISSN: 0143-3857,1469-4417
DOI: 10.1017/etds.2018.79