scholarly journals -algebras of labelled graphs III—-theory computations

2015 ◽  
Vol 37 (2) ◽  
pp. 337-368 ◽  
Author(s):  
TERESA BATES ◽  
TOKE MEIER CARLSEN ◽  
DAVID PASK
Keyword(s):  
Uniqueness Theorem ◽  
Inductive Limit ◽  
Important Class ◽  
Graph Algebras ◽  
Gauge Invariant ◽  
Shift Spaces ◽  
Graph Algebra ◽  
Common Framework ◽  
Definition Of ◽  
Labelled Graphs

In this paper we give a formula for the$K$-theory of the$C^{\ast }$-algebra of a weakly left-resolving labelled space. This is done by realizing the$C^{\ast }$-algebra of a weakly left-resolving labelled space as the Cuntz–Pimsner algebra of a$C^{\ast }$-correspondence. As a corollary, we obtain a gauge-invariant uniqueness theorem for the$C^{\ast }$-algebra of any weakly left-resolving labelled space. In order to achieve this, we must modify the definition of the$C^{\ast }$-algebra of a weakly left-resolving labelled space. We also establish strong connections between the various classes of$C^{\ast }$-algebras that are associated with shift spaces and labelled graph algebras. Hence, by computing the$K$-theory of a labelled graph algebra, we are providing a common framework for computing the$K$-theory of graph algebras, ultragraph algebras, Exel–Laca algebras, Matsumoto algebras and the$C^{\ast }$-algebras of Carlsen. We provide an inductive limit approach for computing the$K$-groups of an important class of labelled graph algebras, and give examples.

scholarly journals Applications of the Gauge-invariant uniqueness theorem for graph algebras

2002 ◽  
Vol 66 (1) ◽  
pp. 57-67 ◽  
Author(s):  
Teresa Bates
Keyword(s):  
Fixed Point ◽  
Uniqueness Theorem ◽  
Directed Graphs ◽  
Cartesian Product ◽  
Graph Algebras ◽  
Gauge Invariant ◽  
Shift Equivalence ◽  
Product Graphs ◽  
Cartesian Product Graphs ◽  
Fixed Point Algebra

We give applications of the gauge-invariant uniqueness theorem, which states that the Cuntz-Krieger algebras of directed graphs are characterised by the existence of a canonical action of . We classify the C*-algebras of higher order graphs, identify the C*-algebras of cartesian product graphs with a certain fixed point algebra and investigate a relation called elementary shift equivalence on graphs and its effect on the associated graph C*-algebras.

Psychological Scaling of Data Obtained on Questionnaires about Career Choices at A Teacher's College

1974 ◽  
Vol 1 (2) ◽  
pp. 58-67
Author(s):  
Desmond Broomes
Keyword(s):  
Career Choices ◽  
Important Class ◽  
Definition Of

Measurement problems pervade most data obtained on questionnaires. One important class of problems seems to reside in the nature of measurement, and may be identified through a study of a definition of measure­ment.

Security of Dependable Systems

2012 ◽  
pp. 230-264 ◽  
Author(s):  
Naveed Ahmed ◽  
Christian Damsgaard Jensen
Keyword(s):  
Stochastic Process ◽  
Open Problem ◽  
Development Process ◽  
Traditional View ◽  
Clear Definition ◽  
Security Attacks ◽  
Dependable Systems ◽  
Broad Concept ◽  
Common Framework ◽  
Definition Of

Security and dependability are crucial for designing trustworthy systems. The approach “security as an add-on” is not satisfactory, yet the integration of security in the development process is still an open problem. Especially, a common framework for specifying dependability and security is very much needed. There are many pressing challenges however; here, we address some of them. Firstly, security for dependable systems is a broad concept and traditional view of security, e.g., in terms of confidentiality, integrity and availability, does not suffice. Secondly, a clear definition of security in the dependability context is not agreed upon. Thirdly, security attacks cannot be modeled as a stochastic process, because the adversary’s strategy is often carefully planned. In this chapter, we explore these challenges and provide some directions toward their solutions.

scholarly journals Graph algebras and orbit equivalence

2015 ◽  
Vol 37 (2) ◽  
pp. 389-417 ◽  
Author(s):  
NATHAN BROWNLOWE ◽  
TOKE MEIER CARLSEN ◽  
MICHAEL F. WHITTAKER
Keyword(s):  
Directed Graphs ◽  
Orbit Equivalence ◽  
Graph Algebras ◽  
Orbit Equivalent ◽  
Markov Shifts ◽  
Graph Algebra ◽  
Arbitrary Graphs ◽  
Reverse Implication

We introduce the notion of orbit equivalence of directed graphs, following Matsumoto’s notion of continuous orbit equivalence for topological Markov shifts. We show that two graphs in which every cycle has an exit are orbit equivalent if and only if there is a diagonal-preserving isomorphism between their $C^{\ast }$-algebras. We show that it is necessary to assume that every cycle has an exit for the forward implication, but that the reverse implication holds for arbitrary graphs. As part of our analysis of arbitrary graphs $E$ we construct a groupoid ${\mathcal{G}}_{(C^{\ast }(E),{\mathcal{D}}(E))}$ from the graph algebra $C^{\ast }(E)$ and its diagonal subalgebra ${\mathcal{D}}(E)$ which generalises Renault’s Weyl groupoid construction applied to $(C^{\ast }(E),{\mathcal{D}}(E))$. We show that ${\mathcal{G}}_{(C^{\ast }(E),{\mathcal{D}}(E))}$ recovers the graph groupoid ${\mathcal{G}}_{E}$ without the assumption that every cycle in $E$ has an exit, which is required to apply Renault’s results to $(C^{\ast }(E),{\mathcal{D}}(E))$. We finish with applications of our results to out-splittings of graphs and to amplified graphs.

scholarly journals Graph varieties containing Murskii's groupoid

1989 ◽  
Vol 39 (2) ◽  
pp. 265-276
Author(s):  
R. Pöschel
Keyword(s):  
Finitely Based ◽  
Graph Algebras ◽  
Undirected Graphs ◽  
Graph Algebra ◽  
Subvariety Lattice ◽  
As Graph ◽  
Graph Varieties ◽  
Nonfinitely Based

In this paper varieties are investigated which are generated by graph algebras of undirected graphs and—in most cases—contain Murskii's groupoid (that is the graph algebra of the graph with two adjacent vertices and one loop). Though these varieties are inherently nonfinitely based, they can be finitely based as graph varieties (finitely graph based) like, for example, the varitey generated by Murskii's groupoid. Many examples of nonfinitely based graph varities containing Murskii's groupoid are given, too. Moreover, the coatoms in the subvariety lattice of the graph variety of all undirected graphs are described. There are two coatoms and they are finitely graph based.

TOPOLOGICAL QUIVERS

2005 ◽  
Vol 16 (07) ◽  
pp. 693-755 ◽  
Author(s):  
PAUL S. MUHLY ◽  
MARK TOMFORDE
Keyword(s):  
Uniqueness Theorem ◽  
Directed Graphs ◽  
Algebra Structure ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Gauge Invariant ◽  
C Algebras ◽  
Natural Analogues ◽  
General Perspective ◽  
The Ideal

Topological quivers are generalizations of directed graphs in which the sets of vertices and edges are locally compact Hausdorff spaces. Associated to such a topological quiver [Formula: see text] is a C*-correspondence, and from this correspondence one may construct a Cuntz–Pimsner algebra [Formula: see text]. In this paper we develop the general theory of topological quiver C*-algebras and show how certain C*-algebras found in the literature may be viewed from this general perspective. In particular, we show that C*-algebras of topological quivers generalize the well-studied class of graph C*-algebras and in analogy with that theory much of the operator algebra structure of [Formula: see text] can be determined from [Formula: see text]. We also show that many fundamental results from the theory of graph C*-algebras have natural analogues in the context of topological quivers (often with more involved proofs). These include the gauge-invariant uniqueness theorem, the Cuntz–Krieger uniqueness theorem, descriptions of the ideal structure, and conditions for simplicity.

scholarly journals A FUNCTORIAL APPROACH TO THE C*-ALGEBRAS OF A GRAPH

2002 ◽  
Vol 13 (03) ◽  
pp. 245-277 ◽  
Author(s):  
JACK SPIELBERG
Keyword(s):  
Structural Properties ◽  
Inductive Limit ◽  
Directed Graphs ◽  
Graph Algebras ◽  
C Algebras ◽  
Injective Homomorphisms ◽  
Functorial Approach

A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to the category of C*-algebras with injective *-homomorphisms. The resulting C*-algebras are identified as Toeplitz graph algebras. Graph algebras are proved to have inductive limit decompositions over any family of subgraphs with union equal to the whole graph. The construction is used to prove various structural properties of graph algebras.

scholarly journals Gauge invariant definition of the jet quenching parameter

2013 ◽  
Vol 2013 (2) ◽  
Author(s):  
Michael Benzke ◽  
Nora Brambilla ◽  
Miguel A. Escobedo ◽  
Antonio Vairo
Keyword(s):  
Jet Quenching ◽  
Gauge Invariant ◽  
Definition Of ◽  
Invariant Definition
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