Related papers: General Non-Commutative Locally Compact Locally Ha…

We extend previous results on noncommutative recurrence in unital *-algebras over the integers, to the case where one works over locally compact Hausdorff groups. We derive a generalization of Khintchine's recurrence theorem, as well as a…

We study the link between a compact hypersurface in $\P^{n+1}$ and the set of all its tangent planes. In this context, we identify $\P^{n+1}$ to the set of linear subspaces of codimension one by orthogonal complementarity. This gives rise…

The K-theoretic analog of Spanier-Whitehead duality for noncommutative C*-algebras is shown to hold for the Ruelle algebras associated to irreducible Smale spaces. This had previously been proved only for shifts of finite type. Implications…

ASD (Abstract Stone Duality) is a re-axiomatisation of general topology in which the topology on a space is treated, not as an infinitary lattice, but as an exponential object of the same category as the original space, with an associated…

Let $C$ be a differential graded coalgebra, $ \bar\Omega C$ the Adams cobar construction and $C^\vee$ the dual algebra. We prove that for a large class of coalgebras $C$ there is a natural isomorphism of Gerstenhaber algebras between the…

We use compactifications of C*-algebras to introduce noncommutative coarse geometry. We transfer a noncommutative coarse structure on a C*-algebra with an action of a locally compact Abelian group by translations to Rieffel deformations and…

The standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this paper, we describe a choice-free…

We consider discontinuous operations of a group $G$ on a contractible $n$-dimensional manifold $X$. Let $E$ be a finite dimensional representation of $G$ over a field $k$ of characteristics 0. Let $\mathcal{E}$ be the sheaf on the quotient…

In 1962, H. de Vries proved a duality theorem for the category {\bf HC} of compact Hausdorff spaces and continuous maps. The composition of the morphisms of the dual category obtained by him differs from the set-theoretic one. Here we…

Classification of quantum spinor fields according to quantum bilinear covariants is introduced in a context of quantum Clifford algebras on Minkowski spacetime. Once the bilinear covariants are expressed in terms of algebraic spinor fields,…

Topological T-duality is a transformation taking a gerbe on a principal torus bundle to a gerbe on a principal dual-torus bundle. We give a new geometric construction of T-dualization, which allows the duality to be extended in following…

Every partial algebra is the colimit of its total subalgebras. We prove this result for partial Boolean algebras (including orthomodular lattices) and the new notion of partial C*-algebras (including noncommutative C*-algebras), and…

The Heisenberg double of a Hopf algebra may be regarded as a quantum analogue of the cotangent bundle of a Lie group. Quantum duality principle describes relations between a Hopf algebra, its dual, and their Heisenberg double in a way which…

We study generalized complex structures and $T$-duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gualtieri map. Such a construction is called "Infinitesimal…

The classification of emergent spinor fields according to modified bilinear covariants is scrutinized, in spacetimes with nontrivial topology, which induce inequivalent spin structures. Extended Clifford algebras, constructed by equipping…

The self-duality of the paracyclic category is extended to a certain class of homotopy categories of (2,1)-categories. These generalise the orbit category of a group and are associated to certain self-dual preorders equipped with a presheaf…

We establish a topological duality for bounded lattices. The two main features of our duality are that it generalizes Stone duality for bounded distributive lattices, and that the morphisms on either side are not the standard ones. A…

In this paper, we formulate and prove a version of the Stone-von Neumann Theorem for every $ C^{\ast} $-dynamical system of the form $ (G,\mathbb{K}(\mathcal{H}),\alpha) $, where $ G $ is a locally compact Hausdorff abelian group and $…

We show that the locally strongly sober spaces are exactly the coherent sober spaces that are weakly Hausdorff in the sense of Keimel and Lawson. This allows us to describe their Stone duals explicitly. As another application, we show that…

We give functorial recipes to get, out of any Hopf algebra over a field, two pairs of Hopf algebras which have some geometrical content. When the ground field has characteristic zero, the first pair is made by a function algebra over a…