Related papers: Comment on the Surface Exponential for Tensor Fiel…

We define and study analogues of exponentials for functions on noncommutative two-tori that depend on a choice of a complex structure. The major difference with the commutative case is that our noncommutative exponentials can be defined…

We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…

In this paper, we derive formal general formulas for noncommutative exponentiation and the exponential function, while also revisiting an unrecognized, and yet powerful theorem. These tools are subsequently applied to derive counterparts…

The main contribution of this note is to establish a framework to extend results of tensor functions over specific field to general field. As a consequence of this framework, we extend the existing work to more general settings: \emph{(1)}…

We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E_n(n). We then consider "tensor gauge fields" coupled to…

We go on with the definition of the theory of the non--Abelian two--tensor fields and find the gauge transformation rules and curvature tensor for them. To define the theory we use the surface {\it exponent} proposed in hep--th/0503234. We…

We investigate exponential sums over singular binary quartic forms, proving an explicit formula for the finite field Fourier transform of this set. Our formula shares much in common with analogous formulas proved previously for other vector…

The analysis of 3D symmetric second-order tensor fields often relies on topological features such as degenerate tensor lines, neutral surfaces, and their generalization to mode surfaces, which reveal important structural insights into the…

For central simple algebras of exponent $2$ over fields of characteristic $2$ and $2$-cohomological dimension equal to $2$, we study the adapted decomposition to some multiquadratic extensions of the base field. Several remarkable…

In this paper we introduce an intermediate field representation for random matrices and random tensors with positive (stable) interactions of degree higher than 4. This representation respects the symmetry axis responsible for positivity.…

A translational surface is a tensor product surface constructed from two space curves by translating one along the other. These surfaces are common within geometric modeling and, since their description is parametric, it is desirable to…

In this article we extend the notion of determinantal representation of hypersurfaces to the determinantal representation of sections of the determinant line bundle of a vector bundle. We give several examples, and prove some necessary…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

We introduce the notion of biconservative hypersurfaces, that is hypersurfaces with conservative stress-energy tensor with respect to the bienergy. We give the (local) classification of biconservative surfaces in 3-dimensional space forms.

Let $M$ be an odd-dimensional Euclidean space endowed with a contact 1-form $\alpha$. We investigate the space of symmetric contravariant tensor fields on $M$ as a module over the Lie algebra of contact vector fields, i.e. over the Lie…

Based on some previous results, one gives a general formula for introducing electromagnetic multipole expansions in terms of symmetric and traceless cartesian tensors.

Two distinct systems of commutative complex numbers in n dimensions are described, of polar and planar types. Exponential forms of n-complex numbers are given in each case, which depend on geometric variables. Azimuthal angles, which are…

We develop a new setting for the exponential principle in the context of multisort species, where indecomposable objects are generated intrinsically instead of being given in advance. Our approach uses the language of functors and natural…

We consider tensor grammars, which are an example of \commutative" grammars, based on the classical (rather than intuitionistic) linear logic. They can be seen as a surface representation of abstract categorial grammars ACG in the sense…

Let A be a central simple algebra over a field F. Let k_1,\ldots, k_r be cyclic extensions of F such that k_1\otimes_F\cdots \otimes_F k_r is a field. We investigate conditions under which A is a tensor product of symbol algebras where each…