Related papers: Duality of $W^*$-correspondences and applications

We define a notion of strong shift equivalence for $C^*$-correspondences and show that strong shift equivalent $C^*$-correspondences have strongly Morita equivalent Cuntz-Pimsner algebras. Our analysis extends the fact that strong shift…

We extend Morita theory to abelian categories by using wide Morita contexts. Several equivalence results are given for wide Morita contexts between abelian categories, widely extending equivalence theorems for categories of modules and…

Based on the localization algebras of Yu, and their subsequent analysis by Qiao and Roe, we give a new picture of KK-theory in terms of time-parametrized families of (locally) compact operators that asymptotically commute with appropriate…

One can view contraction operators given by a canonical model of Sz.-Nagy and Foias as being defined by a quotient module where the basic building blocks are Hardy spaces. In this note we generalize this framework to allow the Bergman and…

This is a general introduction to duality in field theories. The existence and breaking of global symmetries is used as a guideline to systematically prove duality between different field theories. Systems discussed include abelian and…

A theorem of Muhly-Renault-Williams states that if two locally compact groupoids with Haar system are Morita equivalent, then their associated convolution C*-algebras are strongly Morita equivalent. We give a new proof of this theorem for…

We introduce a notion of ideal-related K-theory for rings, and use it to prove that if two complex Leavitt path algebras are Morita equivalent (respectively, isomorphic), then the ideal-related K-theories (respectively, the unital…

We study the question of whether or not contractive representations of logmodular algebras are completely contractive. We prove that a 2-contractive representation of a logmodular algebra extends to a positive map on the enveloping…

Given C*-algebras A and B and an imprimitivity A-B-bimodule X, we construct an explicit isomorphism X_* : K_i(A) --> K_i(B) where K_i denote the complex K-theory functors for i=0, 1. Our techniques do not require separability nor existence…

We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]

We consider two inclusions of $C^*$-algebras whose small $C^*$-algebras have approximate units of the large $C^*$-algebras and their two spaces of all bounded bimodule linear maps. We suppose that the two inclusions of $C^*$-algebras are…

Making use of a recent result of Borchers, an algebraic version of the Bisognano-Wichmann theorem is given for conformal quantum field theories, i.e. the Tomita-Takesaki modular group associated with the von Neumann algebra of a wedge…

In this paper, we give a way to define the Howe correspondences for the similitudes groups over p-adic fields by following the work of Brooks Roberts on the groups (GSp, GO).

We show that any continuous partial action on a topological space has a unique enveloping action, i.e. it is the restriction of a global action. In the case of C^*-algebras we prove that any partial action has an enveloping action up to…

This paper uses monads and comonads to establish a certain type of equivalence between two subcategories, one reflective and one coreflective, in a category whose objects represent compactifications of non-compact locally compact Hausdorff…

Classical Spanier-Whitehead duality was introduced for the stable homotopy category of finite CW complexes. Here we provide a comprehensive treatment of a noncommutative version, termed Spanier-Whitehead $K$-duality, which is defined on the…

We present a constructive proof of Gelfand duality for C*-algebras by reducing the problem to Gelfand duality for real C*-algebras.

It is shown, at the level of the classical action, that the Wess-Zumino-Witten-Novikov model is equivalent to a combined BF theory and a Chern-Simons action in the presence of a unique boundary term. This connection relies on the techniques…

We develop Morita theory for finitary additive 2-representations of finitary 2-categories. As an application we describe Morita equivalence classes for 2-categories of projective functors associated to finite dimensional algebras and for…

Given two locally compact Hausdorff groupoids $G$ and $H$ and a $(G,H)$-equivalence $Z$, one can construct the associated linking groupoid $L$. This is reminiscent of the linking algebra for Morita equivalent $C^*$-algebras. Indeed, Sims…