Related papers: Quantales as geometric objects: symmetry beyond gr…
The purpose of this paper is to present the notion of quotient of supergroups in different categories using the unified treatment of the functor of points and to examine some physically interesting examples.
We consider some integral-geometric quantities that have recently arisen in harmonic analysis and elsewhere, derive some sharp geometric inequalities relating them, and place them in a wider context.
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
In this paper we characterize the projective modules over an arbitrary quantale, and then we apply such a characterization in order to define the K_0 group of a quantale. Then we study congruences of quantales and quantale modules by means…
We describe geometrically the classical and quantum inhomogeneous groups $G_0=(SL(2, \BbbC)\triangleright \BbbC^2)$ and $G_1=(SL(2, \BbbC)\triangleright \BbbC^2)\triangleright \BbbC$ by studying explicitly their shape algebras as a spaces…
This is a survey paper based on my talk at the Workshop on Orbifolds and String Theory, the goal of which was to explain the role of groupoids and their classifying spaces as a foundation for the theory of orbifolds.
A comparison on some facts concerning the geometric quantization of symplectic manifolds is presented here. Criticism, facts and improvements on the sophisticated theory of geometric quantization are presented touching briefly, all the…
The quantum completion of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes an analogous…
Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given a groupoid $G\rightrightarrows \Omega$ associated with a…
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…
The thesis is devoted to abstract, geometric and symmetric aspects of modern elementary particle theories. A new direction in constructing supersymmetric and superstring models based on consequent and strong consideration and inclusion of…
It is the goal of this article to extend the notion of quantization from the standard interpretation focused on non-commuting observables defined starting from classical analogues, to the topological equivalents defined in terms of…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
We give a survey of some known results and of the many open questions in the study of generic phenomena in geometrically interesting groups.
In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…
We review known and we present new results on three types of short distance structures of observables which typically appear in studies of quantum group related algebras. In particular, one of the short distance structures is shown to…
These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…
We outline the main features of the definitions and applications of crossed complexes and cubical $\omega$-groupoids with connections. These give forms of higher homotopy groupoids, and new views of basic algebraic topology and the…
Quantiles are a fundamental concept in probability and theoretical statistics and a daily tool in their applications. While the univariate concept of quantiles is quite clear and well understood, its multivariate extension is more…