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Full-Text Articles in Social and Behavioral Sciences
Higher Order Or Fractional Order Hardy-Sobolev Type Equations, Wenxiong Chen, Yanqin Fang
Higher Order Or Fractional Order Hardy-Sobolev Type Equations, Wenxiong Chen, Yanqin Fang
Faculty of Engineering and Information Sciences - Papers: Part A
In this paper we consider the following higher order or fractional order Hardy-Sobolev type equation.
Kms States On C*-Algebras Associated To Higher-Rank Graphs, Astrid An Huef, Marcelo Laca, Iain Raeburn, Aidan Sims
Kms States On C*-Algebras Associated To Higher-Rank Graphs, Astrid An Huef, Marcelo Laca, Iain Raeburn, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
Consider a higher rank graph of rank k. Both the Cuntz-Krieger algebra and Toeplitz-Cuntz-Krieger algebra of the graph carry natural gauge actions of the torus Tk, and restricting these guage actions to one parameter subgroups of Tk gives dynamical systems involving actions of the real line. We study the KMS states of these dynamical systems. We find that for large inverse temperatures B, the simplex of KMS B states of the Toeplitz-Cuntz-Krieger algebra has dimension d one less than the number of vertices in the graph. We also show that there is a preferred dynamics for which there is a …
Skew-Products Of Higher-Rank Graphs And Crossed Products By Semigroups, Benjamin Maloney, David Pask, Iain Raeburn
Skew-Products Of Higher-Rank Graphs And Crossed Products By Semigroups, Benjamin Maloney, David Pask, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
We consider a free action of an Ore semigroup on a higher-rank graph, and the induced action by endomorphisms of the C ∗-algebra of the graph. We show that the crossed product by this action is stably isomorphic to the C ∗-algebra of a quotient graph. Our main tool is Laca’s dilation theory for endomorphic actions of Ore semigroups on C ∗-algebras, which embeds such an action in an automorphic action of the enveloping group on a larger C ∗-algebra.
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.
Twisted C-Algebras Associated To Finitely Aligned Higher-Rank Graphs, Aidan Sims, Benjamin Whitehead, Michael Whittaker
Twisted C-Algebras Associated To Finitely Aligned Higher-Rank Graphs, Aidan Sims, Benjamin Whitehead, Michael Whittaker
Faculty of Engineering and Information Sciences - Papers: Part A
We introduce twisted relative Cuntz-Krieger algebras associated to finitely aligned higher-rank graphs and give a comprehensive treatment of their fundamental structural properties. We establish versions of the usual uniqueness theorems and the classification of gauge-invariant ideals. We show that all twisted relative Cuntz- Krieger algebras associated to finitely aligned higher-rank graphs are nuclear and satisfy the UCT, and that for twists that lift to real-valued cocycles, the K-theory of a twisted relative Cuntz-Krieger algebra is independent of the twist. In the final section, we identify a sufficient condition for simplicity of twisted Cuntz-Krieger algebras associated to higher-rank graphs which are …