Related papers: Parallel transports in tensor spaces generated by …
In this paper we explore the connection between tensor algebras and displacement structure. We describe a scattering experiment in this framework, we obtain a realization of the elements of the tensor algebra as transfer maps of a certain…
Tensor distributions and their derivatives are described without assuming the presence of a metric. This provides a natural framework for discussing tensor distributions on manifolds with degenerate metrics, including in particular metrics…
Quantum connections are defined by parallel transport operators acting on a Hilbert space. They transport tangent operators along paths in parameter space. The metric tensor of a Riemannian manifold is replaced by an inner product of pairs…
Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…
This article is a summary of a series of papers to be published where I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable…
The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…
In this short note we give an elementary proof of the fact that connections and their geometric parallel-transport counterpart are equivalent notions.
We characterize all natural linear operations between spaces of differential forms on contact manifolds. Our main theorem says roughly that such operations are built from some algebraic operators which we introduce and the exterior…
We discuss certain ternary algebraic structures appearing more or less naturally in various domains of theoretical and mathematical physics. Far from being exhaustive, this article is intended above all to draw attention to these algebras,…
In this paper we study the representation dimension as well as the derived dimension of the path algebra of an artin algebra over a finite and acyclic quiver.
Following arXiv:0909.5586 and arXiv:1411.4125, we construct two super-extensions of the usual tensor algebra through the super-actions of symmetric groups and Hecke algebras respectively. For each extension, we consider a special type of…
The geometry of parallelizable manifolds (i.e., teleparallelism) is summarized in the language of local frame fields. Some problems in continuum mechanics that relate to the couple-stresses that are produced in the bending and twisting of…
We investigate the validity of the equivalence principle along paths in gravitational theories based on derivations of the tensor algebra over a differentiable manifold. We prove the existence of local bases, called normal, in which the…
A tensor space is a vector space equipped with a finite collection of multi-linear forms. In recent years, a rich theory of infinite dimensional tensor spaces has emerged. In this note, we show that a large class of permutation groups can…
Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…
The most general form of the deviation equations in spaces with linear connection with arbitrary torsion is derived.
Meta-conformal transformations are constructed as dynamical symmetries of the linear transport equation in $d$ spatial dimensions. In one and two dimensions, the associated Lie algebras are infinite-dimensional and isomorphic to the direct…
In this series of papers I examine a special kind of geometric objects that can be defined in space-time --- five-dimensional tangent vectors. Similar objects exist in any other differentiable manifold, and their dimension is one unit…
Usually, mathematical objects have highly parallel interpretations. In this paper, we consider them as sequential constructors of other objects. In particular, we prove that every reflexive directed graph can be interpreted as a program…
Scalar-tensor theories offer the prospect of explaining the cosmological evolution of the Universe through an effective description of dark energy as a quantity with a non-trivial evolution. In this work, we investigate this feature of…