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Full-Text Articles in Engineering
The Extension Class And Kms States For Cuntz-Pimsner Algebras Of Some Bi-Hilbertian Bimodules, Adam C. Rennie, David I. Robertson, Aidan Sims
The Extension Class And Kms States For Cuntz-Pimsner Algebras Of Some Bi-Hilbertian Bimodules, Adam C. Rennie, David I. Robertson, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
For bi-Hilbertian A-bimodules, in the sense of Kajiwara-Pinzari-Watatani, we construct a Kasparov module representing the extension class defining the Cuntz-Pimsner algebra. The construction utilises a singular expectation which is defined using the C*-module version of the Jones index for bi-Hilbertian bimodules. The Jones index data also determines a novel quasi-free dynamics and KMS states on these Cuntz-Pimsner algebras.
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.
Equilibrium States On The Cuntz-Pimsner Algebras Of Self-Similar Actions, Marcelo Laca, Iain Raeburn, Jacqui Ramagge, Michael Whittaker
Equilibrium States On The Cuntz-Pimsner Algebras Of Self-Similar Actions, Marcelo Laca, Iain Raeburn, Jacqui Ramagge, Michael Whittaker
Faculty of Engineering and Information Sciences - Papers: Part A
We consider a family of Cuntz-Pimsner algebras associated to self-similar group actions, and their Toeplitz analogues. Both families carry natural dynamics implemented by automorphic actions of the real line, and we investigate the equilibrium states (the KMS states) for these dynamical systems. We find that for all inverse temperatures above a critical value, the KMS states on the Toeplitz algebra are given, in a very concrete way, by traces on the full group algebra of the group. At the critical inverse temperature, the KMS states factor through states of the Cuntz-Pimsner algebra; if the self-similar group is contracting, then the …
Exel's Crossed Product And Relative Cuntz-Pimsner Algebras, Nathan Brownlowe, Iain Raeburn
Exel's Crossed Product And Relative Cuntz-Pimsner Algebras, Nathan Brownlowe, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
We consider Exel's new construction of a crossed product of a $C^*$-algebra $A$ by an endomorphism $\alpha$. We prove that this crossed product is universal for an appropriate family of covariant representations, and we show that it can be realised as a relative Cuntz-Pimsner algbera. We describe a necessary and sufficient condition for the canonical map from $A$ into the crossed product to be injective, and present several examples to demonstrate the scope of this result. We also prove a gauge-invariant uniqueness theorem for the crossed product.
Cuntz-Krieger Algebras Of Infinite Graphs And Matrices, Iain Raeburn, Wojciech Szymanski
Cuntz-Krieger Algebras Of Infinite Graphs And Matrices, Iain Raeburn, Wojciech Szymanski
Faculty of Engineering and Information Sciences - Papers: Part A
We show that the Cuntz-Krieger algebras of infinite graphs and infinite {0,1}-matrices can be approximated by those of finite graphs. We then use these approximations to deduce the main uniqueness theorems for Cuntz-Krieger algebras and to compute their K-theory. Since the finite approximating graphs have sinks, we have to calculate the K-theory of Cuntz-Krieger algebras of graphs with sinks, and the direct methods we use to do this should be of independent interest.
Representations Of Cuntz-Pimsner Algebras, Neal J. Fowler, Paul S. Muhly, Iain Raeburn
Representations Of Cuntz-Pimsner Algebras, Neal J. Fowler, Paul S. Muhly, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
Let X be a Hilbert bimodule over a C * -algebra A. We analyse the structure of the associated Cuntz-Pimsner algebra X and related algebras using representation-theoretic methods. In particular, we study the ideals (I) in X induced by appropriately invariant ideals I in A, and identify the quotients X/(I) as relative Cuntz-Pimsner algebras of Muhly and Solel. We also prove a gauge-invariant uniqueness theorem for X, and investigate the relationship between X and an alternative model proposed by Doplicher, Pinzari and Zuccante.
Representations Of Finite Groups And Cuntz-Krieger Algebras, M Mann, Iain Raeburn, C Sutherland
Representations Of Finite Groups And Cuntz-Krieger Algebras, M Mann, Iain Raeburn, C Sutherland
Faculty of Engineering and Information Sciences - Papers: Part A
We investigate the structure of the C*-algebras (9ρ constructed by Doplicher and Roberts from the intertwining operators between the tensor powers of a representation ρ of a compact group. We show that each Doplicher-Roberts algebra is isomorphic to a corner in the Cuntz-Krieger algebra (9A of a {0,1}-matrix A = Aρ associated to ρ. When the group is finite, we can then use Cuntz's calculation of the K-theory of (9A to compute K*((9ρ).