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Full-Text Articles in Social and Behavioral Sciences
An Analytic Approach To Spectral Flow In Von Neumann Algebras, M-T Benameur, Alan L. Carey, John Phillips, Adam C. Rennie, Fyodor A. Sukochev, K P. Wojciechowski
An Analytic Approach To Spectral Flow In Von Neumann Algebras, M-T Benameur, Alan L. Carey, John Phillips, Adam C. Rennie, Fyodor A. Sukochev, K P. Wojciechowski
Faculty of Engineering and Information Sciences - Papers: Part A
The analytic approach to spectral flow is about ten years old. In that time it has evolved to cover an ever wider range of examples. The most critical extension was to replace Fredholm operators in the classical sense by Breuer-Fredholm operators in a semifinite von Neumann algebra. The latter have continuous spectrum so that the notion of spectral flow turns out to be rather more difficult to deal with. However quite remarkably there is a uniform approach in which the proofs do not depend on discreteness of the spectrum of the operators in question. The first part of this paper …
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.
Subquotients Of Hecke C*-Algebras, Nathan Brownlowe, Nadia Larsen, Ian Putnam, Iain Raeburn
Subquotients Of Hecke C*-Algebras, Nathan Brownlowe, Nadia Larsen, Ian Putnam, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
We realize the Hecke C*-algebra CQ of Bost and Connes as a direct limit of Hecke C*-algebras which are semigroup crossed products by NF, for F a finite set of primes. For each approximating Hecke C*-algebra we describe a composition series of ideals. In all cases there is a large type I ideal and a commutative quotient, and the intermediate subquotients are direct sums of simple C*-algebras. We can describe the simple summands as ordinary crossed products by actions of ZS for S a finite set of primes. …
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.
Classification Theorems For The C*-Algebras Of Graphs With Sinks, Iain Raeburn, Mark Tomforde, Dana Williams
Classification Theorems For The C*-Algebras Of Graphs With Sinks, Iain Raeburn, Mark Tomforde, Dana Williams
Faculty of Engineering and Information Sciences - Papers: Part A
We consider graphs E which have been obtained by adding one or more sinks to a fixed directed graph G. We classify the C*-algebra of E up to a very strong equivalence relation, which insists, loosely speaking, that C*(G) is kept fixed. The main invariants are vectors WE: G0 → which describe how the sinks are attached to G; more precisely, the invariants are the classes of the WE in the cokernel of the map A – I, where A is the adjacency matrix of the graph …
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.
Higher-Rank Graphs And Their C*-Algebras, Iain Raeburn, Aidan Sims, Trent Yeend
Higher-Rank Graphs And Their C*-Algebras, Iain Raeburn, Aidan Sims, Trent Yeend
Faculty of Engineering and Information Sciences - Papers: Part A
We consider the higher-rank graphs introduced by Kumjian and Pask as models for higher-rank Cuntz-Krieger algebras. We describe a variant of the Cuntz-Krieger relations which applies to graphs with sources, and describe a local convexity condition which characterises the higher-rank graphs that admit a nontrivial Cuntz-Krieger family. We then prove versions of the uniqueness theorems and classifications of ideals for the C*-algebras generated by Cuntz-Krieger families.
Induced C*-Algebras, Coactions And Equivariance In The Symmetric Imprimitivity Theorem, Siegfried Echterhoff, Iain Raeburn
Induced C*-Algebras, Coactions And Equivariance In The Symmetric Imprimitivity Theorem, Siegfried Echterhoff, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
The symmetric imprimitivity theorem provides a Morita equivalence between two crossed products of induced C*-algebras and includes as special cases many other important Morita equivalences such as Green's imprimitivity theorem. We show that the symmetric imprimitivity theorem is compatible with various inflated actions and coactions on the crossed products.
The C*-Algebras Of Row-Finite Graphs, Teresa Bates, David Pask, Iain Raeburn, Wojciech Szymanski
The C*-Algebras Of Row-Finite Graphs, Teresa Bates, David Pask, Iain Raeburn, Wojciech Szymanski
Faculty of Engineering and Information Sciences - Papers: Part A
We prove versions of the fundamental theorems about Cuntz-Krieger algebras for the C*-algebras of row-finite graphs: directed graphs in which each vertex emits at most finitely many edges. Special cases of these results have previously been obtained using various powerful machines; our main point is that direct methods yield sharper results more easily.
The C*-Algebras Of Infinite Graphs, Neal J. Fowler, Marcelo Laca, Iain Raeburn
The C*-Algebras Of Infinite Graphs, Neal J. Fowler, Marcelo Laca, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
We associate C*-algebras to infinite directed graphs that are not necessarily locally finite. By realizing these algebras as Cuntz-Krieger algebras in the sense of Exel and Laca, we are able to give criteria for their uniqueness and simplicity, generalizing results of Kumjian, Pask, Raeburn, and Renault for locally finite directed graphs.
Lie Algebras Of Cohomological Codimension One, Grant F. Armstrong, Grant Cairns, Gunky Kim
Lie Algebras Of Cohomological Codimension One, Grant F. Armstrong, Grant Cairns, Gunky Kim
Faculty of Engineering and Information Sciences - Papers: Part A
We show that if g is a finite dimensional real Lie algebra, then g has cohomological dimension cd(g) = dim(g) - 1 if and only if g is a unimodular extension of the two-dimensional non-Abelian Lie algebra aff.
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.
Induced C*-Algebras And Landstad Duality For Twisted Coactions, John C. Quigg, Iain Raeburn
Induced C*-Algebras And Landstad Duality For Twisted Coactions, John C. Quigg, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
No abstract provided.
Crossed Products By Semigroups Of Endomorphisms And The Toeplitz Algebras Of Ordered Groups, Sriwulan Adji, Marcelo Laca, May Nilsen, Iain Raeburn
Crossed Products By Semigroups Of Endomorphisms And The Toeplitz Algebras Of Ordered Groups, Sriwulan Adji, Marcelo Laca, May Nilsen, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
No abstract provided.
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).
On The Structure Of Twisted Group C*-Algebras, Judith A. Packer, Iain Raeburn
On The Structure Of Twisted Group C*-Algebras, Judith A. Packer, Iain Raeburn
Faculty of Engineering and Information Sciences - Papers: Part A
No abstract provided.