Related papers: Duality of $W^*$-correspondences and applications
The paper presents a detailed description of duality for braided algebras, coalgebras, bialgebras, Hopf algebras and their modules and comodules in the infinite setting. Assuming that the dual objects exist, it is shown how a given braiding…
Taking advantage of the quantale-theoretic description of \'etale groupoids we study principal bundles, Hilsum-Skandalis maps, and Morita equivalence in terms of modules on inverse quantal frames. The Hilbert module description of quantale…
Various aspects of Morita theory of deformed algebras and in particular of star product algebras on general Poisson manifolds are discussed. We relate the three flavours ring-theoretic Morita equivalence, $^*$-Morita equivalence, and strong…
We study the derived invariance of the cohomology theories $Hoch^*$, $H^*$ and $HC^*$ associated to coalgebras over a field. We prove a theorem characterizing derived equivalences. As particular cases, it describes the two following…
The author provides some definitions and structural results about Fell bundles, defined as C^*-algebra bundles over topological groupoids. Such bundles are a mutual generalization of semi-direct products of groups with C^*-algebras and…
We explore a curious type of equivalence between certain pairs of reflective and coreflective subcategories. We illustrate with examples involving noncommutative duality for C*-dynamical systems and compact quantum groups, as well as…
We introduce twisted topological correspondences, which generalize both Katsura's topological correspondences as well as the twisted topological graphs introduced by Li. We show that, up to isomorphism, they are in bijection with certain…
After embedding the objects quasifolds into the category {Diffeology}, we associate a C*-agebra with every atlas of any quasifold, and show how different atlases give Morita equivalent algebras. This builds a new bridge between diffeology…
We have generalised the notion of categorical theory in model theory to the context of coherent theories. We prove a duality result between the full sub-2-category of pretopoi which are categorical, and the 2-category of profinite monoids.…
In this note, we will define the formulas of curvature and it's covariant derivatives for holomorphic curves on C*-algebras for the multivariable case. As applications, the unitarily and similarly classification theorems for holomorphic…
These are some notes I wrote for the summer school "Symbolic dynamics and homeomorphisms of the Cantor set" at the University of Copenhagen, 23 - 27 June 2008. The notes contain the definition of the C*-algebra associated to a shift space…
We give a proof of the Howe duality conjecture for the (almost) equal rank dual pairs in full generality. For arbitrary dual pairs, we prove the irreducibility of the (small) theta lifts for all tempered representations. Our proof works for…
We study a class of duality transformations in generalised Z(2) gauge theories and Ising models on two- and three-dimensional compact lattices. The theories are interpreted algebraically in terms of the structure constants of a…
Structures based on polarities have been used to provide relational semantics for propositional logics that are modelled algebraically by non-distributive lattices with additional operators. This article develops a first order notion of…
Algebras associated with Quantum Electrodynamics and other gauge theories share some mathematical features with T-duality Exploiting this different perspective and some category theory, the full algebra of fermions and bosons can be…
We extend to the context of locally C*-algebras a result of F. Combes [Proc. London Math. Soc. 49(1984), 289-306].
A duality theory of bundles of C$^*$-algebras whose fibres are twisted transformation group algebras is established. Classical T-duality is obtained as a special case, where all fibres are commutative tori, i.e. untwisted group algebras for…
Let $\mathbb{G}$ be a locally compact quantum group, and $A,B$ von Neumann algebras on which $\mathbb{G}$ acts. We refer to these as $\mathbb{G}$-dynamical W$^*$-algebras. We make a study of $\mathbb{G}$-equivariant $A$-$B$-correspondences,…
We prove Howe duality for an exceptional theta correspondence. To that end we exploit a pair of see-saw identities and relate the $K$-types of corresponding representations.
We give a simple generalisation of a theorem of Morita, which leads to a great number of relations among tautological classes on moduli spaces of curves.