Related papers: Generalized forms, vector fields and superspace

In this paper we extend the Lie theory of integration in two different ways. First we consider a finite dimensional Lie algebra of vector fields and discuss the most general conditions under which the integral curves of one of the fields…

The reductions of conformal field theories which lead to generalized abelian cosets are studied. Primary fields and correlation functions of arbitrary abelian coset conformal field theory are explicitly expressed in terms of those of the…

In the main part of this paper a connection is just a fiber projection onto a (not necessarily integrable) distribution or sub vector bundle of the tangent bundle. Here curvature is computed via the Froelicher-Nijenhuis bracket, and it is…

In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established.

A notion of general manifolds is introduced. It covers all usual manifolds in mathematics. Essentially, it is a way how to get a bigger 'fibration' over a site which locally coincides with a given one. An enrichment with generalized…

Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…

In this work, we make new developments in generic cotangent bundle geometries, depending on all phase-space variables. In particular, we will focus on the so-called generalized Hamilton spaces, discussing how the main ingredients of this…

Using supervector fields and graded forms along a morphism, we study the geometry of ordinary differential superequations, extend the formalism of higher order Lagrangian mechanics to the graded context and prove a generalization of…

Generalized Functions play a central role in the understanding of differential equations containing singularities and nonlinearities. Introducing infinitesimals and infinities to deal with these obstructions leads to controversies…

A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…

The Lie algebra of planar vector fields with coefficients from the field of rational functions over an algebraically closed field of characteristic zero is considered. We find all finite-dimensional Lie algebras that can be realized as…

Generalized cycles can be thought of as the extension of form-cycle duality between holomorphic forms and cycles, to meromorphic forms and generalized cycles. They appeared as an ubiquitous tool in the study of spectral curves and…

Frame bundles equipped with a principal connection have their local structure characterised by a 1-form, called the Cartan connection 1-form, which gathers the principal connection form and the soldering form. We introduce generalised frame…

A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…

Based on Colombeau's theory of algebras of generalized functions we introduce the concepts of generalized functions taking values in differentiable manifolds as well as of generalized vector bundle homomorphisms. We study their basic…

This short report establishes some basic properties of smooth vector fields on product manifolds. The main results are: (i) On a product manifold there always exists a direct sum decomposition into horizontal and vertical vector fields.…

The purpose of this paper is to put into a noncommutative context basic notions related to vector fields from classical differential geometry. The manner of exposition is an attempt to make the material as accessible as possible to…

In this paper, we mainly study the generalized Heisenberg-Virasoro algebra. Some structural properties of the Lie algebra are studied.

Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural…

This paper concerns the \textbf{abstract geometry of numbers}: namely the pursuit of certain aspects of geometry of numbers over a suitable class of normed domains. (The standard geometry of numbers is then viewed as geometry of numbers…