Related papers: Loop torsors. Theory and applications

This paper introduces a new approach to the study of certain aspects of Galois module theory by combining ideas arising from the study of the Galois structure of torsors of finite group schemes with techniques coming from relative algebraic…

In an earlier paper of the author, locally compact quantum torsors were defined for locally compact quantum groups, putting into the analytic framework the theory of Galois objects for Hopf algebras. Such quantum torsors allow to deform the…

In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie…

We study a non-pointed version of the notion of torsion theory in the framework of categories equipped with a posetal monocoreflective subcategory such that the coreflector inverts monomorphisms. We explore the connections of such torsion…

We consider spinorial fields in polar form to deduce their respective tensorial connection in various physical situations: we show that in some cases the tensorial connection is a useful tool, instead in other cases it arises as a necessary…

We give explicit and elementary constructions of the categorical extensions of a torus by the circle and discuss an application to loop group extensions. Examples include maximal tori of simple and simply connected compact Lie groups and…

In this note we investigate the problem of existence of a torsor structure for Galois covers of (formal) schemes over a complete discrete valuation ring of residue characteristic $p>0$ in the case of abelian Galois groups of type…

We discuss a concept of loopoid as a non-associative generalization of (Brandt) groupoid. We introduce and study also an interesting class of more general objects which we call semiloopoids. A differential version of loopoids is intended as…

We consider linear systems on toric varieties of any dimension, with invariant base points, giving a characterization of special linear systems. We then make a new conjecture for linear systems on rational surfaces.

We study loop near-rings, a generalization of near-rings, where the additive structure is not necessarily associative. We introduce local loop near-rings and prove a useful detection principle for localness.

The role of automorphisms of infinite-dimensional Lie algebras in conformal field theory is examined. Two main types of applications are discussed; they are related to the enhancement and reduction of symmetry, respectively. The structures…

This is the first in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the "Verlinde ring" of its loop group. In this paper we set up the foundations of twisted…

A Riemann-Poisson Lie group is a Lie group endowed with a left invariant Riemannian metric and a left invariant Poisson tensor which are compatible in the sense introduced in C.R. Acad. Sci. Paris s\'er. {\bf I 333} (2001) 763-768. We study…

We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…

The Linearization Theorem for proper Lie groupoids organizes and generalizes several results for classic geometries. Despite the various approaches and recent works on the subject, the problem of understanding invariant linearization…

The "loop equations" of random matrix theory are a hierarchy of equations born of attempts to obtain explicit formulae for generating functions of map enumeration problems. These equations, originating in the physics of 2-dimensional…

We study tensors on Lie groupoids suitably compatible with the groupoid structure, called {\em multiplicative}. Our main result gives a complete description of these objects only in terms of infinitesimal data. Special cases include the…

In the context of categories equipped with a structure of nullhomotopies, we introduce the notion of homotopy torsion theory. As special cases, we recover pretorsion theories as well as torsion theories in multi-pointed categories and in…

We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We develop their underlying Lie theory, showing how these…

We describe torsion classes in the first cohomology group of $\text{SL}_2(\mathbb{Z})$. In particular, we obtain generalized Dickson's invariants for p-power polynomial rings. Secondly, we describe torsion classes in the zero-th homology…