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Articles 1 - 6 of 6
Full-Text Articles in Social and Behavioral Sciences
The Primitive Ideals Of The Cuntz-Krieger Algebra Of A Row-Finite Higher-Rank Graph With No Sources, Toke Meier Carlsen, Sooran Kang, Jacob Shotwell, Aidan Sims
The Primitive Ideals Of The Cuntz-Krieger Algebra Of A Row-Finite Higher-Rank Graph With No Sources, Toke Meier Carlsen, Sooran Kang, Jacob Shotwell, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We catalogue the primitive ideals of the Cuntz–Krieger algebra of a row-finite higher-rank graph with no sources. Each maximal tail in the vertex set has an abelian periodicity group of finite rank at most that of the graph; the primitive ideals in the Cuntz–Krieger algebra are indexed by pairs consisting of a maximal tail and a character of its periodicity group. The Cuntz–Krieger algebra is primitive if and only if the whole vertex set is a maximal tail and the graph is aperiodic.
Realising The C*-Algebra Of A Higher-Rank Graph As An Exel's Crossed Product, Nathan Brownlowe
Realising The C*-Algebra Of A Higher-Rank Graph As An Exel's Crossed Product, Nathan Brownlowe
Faculty of Engineering and Information Sciences - Papers: Part A
We use the boundary-path space of a finitely-aligned k-graph Lambda to construct a compactly-aligned product system X, and we show that the graph algebra C*(Lambda) is isomorphic to the Cuntz-Nica-Pimsner algebra NO(X). In this setting, we introduce the notion of a crossed product by a semigroup of partial endomorphisms and partially-defined transfer operators by defining it to be NO(X). We then compare this crossed product with other definitions in the literature.
The Two-Prime Analogue Of The Hecke C*-Algebra Of Bost And Connes, Nadia Larsen, Ian Putnam, Iain Raeburn
The Two-Prime Analogue Of The Hecke C*-Algebra Of Bost And Connes, Nadia Larsen, Ian Putnam, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
Let p and q be distinct odd primes. We analyse a semigroup crossed product C * (G p,q) α 2 similar to the semigroup crossed product which models the Hecke C * -algebra of Bost and Connes. We describe a composition series of ideals in C * (G p,q) α 2 , and show that the structure of one of the subquotients reflects interesting number-theoretic information about the multiplicative orders of q in the rings Z/pl Z.
The Toeplitz Algebra Of A Hilbert Bimodule, Neal J. Fowler, Iain Raeburn
The Toeplitz Algebra Of A Hilbert Bimodule, Neal J. Fowler, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
Suppose a C ∗ -algebra A acts by adjointable operators on a Hilbert A -module X. Pimsner constructed a C ∗ -algebra 𝒪 X which includes, for particular choices of X , crossed products of A by Z , the Cuntz algebras 𝒪 n , and the CuntzKrieger algebras 𝒪 B. Here we analyse the representations of the corresponding Toeplitz algebra. One consequence is a uniqueness theorem for the ToeplitzCuntz-Krieger algebras of directed graphs, which includes Cuntz’s uniqueness theorem for 𝒪 ∞.
Cancellation Laws For Bci-Algebra, Atoms And P-Semisimple Bci-Algebras, M W. Bunder
Cancellation Laws For Bci-Algebra, Atoms And P-Semisimple Bci-Algebras, M W. Bunder
Faculty of Engineering and Information Sciences - Papers: Part A
We derive cancellation laws for BCI-algebras and for p-semisimple BCI- algebras, show that the set of all atoms of a BCI-algebra is a p semisimple BCI-algebra and that in a p-semisimple BCI-algebra and = are the same.
Statistical Image Algebra: A Bayesian Approach, Jennifer L. Davidson, Noel A. Cressie
Statistical Image Algebra: A Bayesian Approach, Jennifer L. Davidson, Noel A. Cressie
Faculty of Engineering and Information Sciences - Papers: Part A
A mathematical structure used to express image processing transforms, the AFATL image algebra has proved itself useful in a wide variety of applications. The theoretical foundation for the image algebra includes many important constructs for handling a wide variety of image processing problems: questions relating to linear and nonlinear transforms, including decomposition techniques [9], [5]; mapping of transformations to computer architectures [8], [4]; neural networks [1 1], [6]; recursive transforms [10]; and data manipulation on hexagonal arrays. However, statistical notions have been included only on a very elementary level in [12], and on a more sophisticated level in [2]. In …