Related papers: Compact quantum metric spaces from quantum groups …

We argue that a (slightly) curved space-time probed with a finite resolution, equivalently a finite minimal length, is effectively described by a flat non-commutative space-time. More precisely, a small cosmological constant (so a constant…

We establish two conditions equivalent to coamenability for type I locally compact quantum groups. The first condition is concerned with the spectra of certain convolution operators on the space…

This paper is a short account of the construction of a new class of the infinite-dimensional representations of the quantum groups. The examples include finite-dimensional quantum groups $U_q(\mathfrak{g})$, Yangian $Y(\mathfrak{g})$ and…

We give a partial solution to a long-standing open problem in the theory of quantum groups, namely we prove that all finite-dimensional representations of a wide class of locally compact quantum groups factor through matrix quantum groups…

We consider compact matrix quantum groups whose fundamental corepresentation matrix has entries which are partial isometries with central support. We show that such quantum groups have a simple representation as semi-direct product quantum…

We classify all compact quantum groups whose C*-algebra sits inside that of the free unitary quantum groups $U_{N}^{+}$. In other words, we classify all discrete quantum subgroups of $\widehat{U}_{N}^{+}$, thereby proving a quantum variant…

Using methods coming from non-formal equivariant quantization, we construct in this short note a unitary dual 2-cocycle on a discrete family of quotient groups of subgroups of the affine group of a local field (which is not of…

In this article, we give a definition for measured quantum groupoids. We want to get objects with duality extending both quantum groups and groupoids. We base ourselves on J. Kustermans and S. Vaes' works about locally compact quantum…

In this paper Quantum Mechanics with Fundamental Length is built as a deformation of Quantum Mechanics. To this aim an approach is used which does not take into account commutator deformation as usually it is done, but density matrix…

We describe smooth compactifications of certain families of reductive homogeneous spaces such as group manifolds for classical Lie groups, or pseudo-Riemannian analogues of real hyperbolic spaces and their complex and quaternionic…

We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in \cite{monod} to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we…

For second countable discrete quantum groups, and more generally second countable locally compact quantum groups with trivial scaling group, we show that property (T) is equivalent to every weakly mixing unitary representation not having…

We present the case for a fundamentally discrete quantum spacetime and for Group Field Theories as a candidate consistent description of it, briefly reviewing the key properties of the GFT formalism. We then argue that the outstanding…

We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with…

Let $\ell$ be a length function on a group $G$, and let $M_{\ell}$ denote the operator of pointwise multiplication by $\ell$ on $\bell^2(G)$. Following Connes, $M_{\ell}$ can be used as a ``Dirac'' operator for $C_r^*(G)$. It defines a…

In 2007, G.E. Andrews introduced the $(n+1)$-variable combinatorial generating function $R_n(x_1,x_2,\cdots,x_n;q)$ for ranks of $n$-marked Durfee symbols, an $(n+1)$-dimensional multisum, as a vast generalization to the ordinary…

An exposition of quantum permutation groups where an alternative to the 'Gelfand picture' of compact quantum groups is proposed. This point of view is inspired by algebraic quantum mechanics and posits that states on the algebra of…

In recent years, several quantizations of real manifolds have been studied, in particular from the point of view of Connes' noncommutative geometry. Less is known for complex noncommutative spaces. In this paper, we review some recent…

Spectral triples describe and generalize Riemannian spin geometries by converting the geometrical information into algebraic data, which consist of an algebra $A$, a Hilbert space $H$ carrying a representation of $A$ and the Dirac operator…

Compact quantum groups of face type, as introduced by Hayashi, form a class of compact quantum groupoids with a classical, finite set of objects. Using the notions of a weak multiplier bialgebra and weak multiplier Hopf algebra (resp. due…