Related papers: Groupoid Quantales: a non \'etale setting

We determine the structure of completely inverse AG**-groupoids modulo semilattices of abelian groups and their involutive, idempotent-fixed automorphisms.

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…

We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…

We introduce nonassociative geometric objects generalising naturally Lie groupoids and called (smooth) quasiloopoids and loopoids. We prove that the tangent bundles of smooth loopoids are canonically smooth loopoids again (it is nontrivial…

Let G be a finite group and let S be a G-set. The Burnside ring of G has a natural structure of a lambda-ring. However, a priori the images of S under the lambda-operations can only be computed implicitly. In this paper we establish an…

We show that a (not necessarily Hausdorff) etale, second countable groupoid G with totally disconnected unit space may be reconstructed solely from the algebraic structure of its ample semigroup S. We also show that C*(G) possesses a…

This work is a spin-off of an on-going programme which aims at revisiting the original studies of Lie and Cartan on pseudogroups and geometric structures from a modern perspective. We encode geometric structures induced by transitive Lie…

Let G be a simple complex algebraic group. By using a notion of a G-category we define invariants of tangles with flat G-connections in their complements. We also show that quantized universal enveloping algebras at roots of unity provide…

This work mainly concerns the -- here introduced -- category of $\mathscr Q$-sets and functional morphisms, where $\mathscr Q$ is a commutative semicartesian quantale. We describe, in detail, the limits and colimits of this complete and…

In this paper subcentral (resp., central) idempotent series and composition subcentral (resp., central) idempotent series in an inverse semigroup are introduced and investigated. It is shown that if $S=EG$ is a factorizable inverse monoids…

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these…

Let $K$ be a commutative ring with unit and $S$ an inverse semigroup. We show that the semigroup algebra $KS$ can be described as a convolution algebra of functions on the universal \'etale groupoid associated to $S$ by Paterson. This…

The description of irreducible representations of a group G can be seen as a question in harmonic analysis; namely, decomposing a suitable space of functions on G into irreducibles for the action of G x G by left and right multiplication.…

We construct a new class of finite-dimensional C^*-quantum groupoids at roots of unity q=e^{i\pi/\ell}, with limit the discrete dual of the classical SU(N) for large orders. The representation category of our groupoid turns out to be tensor…

In this paper we introduce the localization construction for quantales. A quantale is a complete semilattice combined with a multiplication. We mimic the notion of filter in a lattice to define multiplicative filters in a quantale, and…

Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…

We start by reviewing the relation between toposes and Grothendieck quantales. We improve results of previous work on this relation by giving both a characterisation of the map from the tensor product of two internal sup-lattices to another…

Let $G$ be a Lie group, with an invariant non-degenerate symmetric bilinear form on its Lie algebra, let $\pi$ be the fundamental group of an orientable (real) surface $M$ with a finite number of punctures, and let $\bold C$ be a family of…

It this note we investigate the structure of the group of \sigma-unitary units in some noncommutative modular group algebras KG, where \sigma is a non-classical ring involution of KG.

We construct a topos of quantum sets and embed into it the classical topos of sets. We show that the internal logic of the topos of sets, when interpreted in the topos of quantum sets, provides the Birkhoff-von Neumann quantum propositional…