Related papers: Subfields of algebraically maximal Kaplansky field…
We classify higher-order Maxwell-Einstein theories linear in the curvature tensor and quadratic in the derivatives of the electromagnetic field strength whose kinetic matrices are degenerate. This provides a generalisation of quadratic…
Let $A$ be an abelian variety over a number field. The connected monodromy field of $A$ is the minimal field over which the images of all the $\ell$-adic torsion representations have connected Zariski closure. We show that for all even $g…
Starting from $E_{11}$ and the space-time translations we construct an algebra that promotes the global $E_{11}$ symmetries to local ones, and consider all its possible massive deformations. The Jacobi identities imply that such…
We study the maximal rank in affine subspaces of symmetric or alternating matrices, in terms of the matching numbers of certain associated graphs. Applications include simple proofs of upper bounds on the dimension of such subspaces in…
One of the main contributions which Volker Weispfenning made to mathematics is related to Groebner bases theory. In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational…
We give tables of noncompact real forms of maximal reductive subalgebras of complex simple Lie algebras of rank up to 8. These were obtained by computational methods that we briefly describe. We also discuss applications in theoretical…
We give an algorithm that constructs a minimal set of polynomials defining all extension of a $(\pi)$-adic field with given, inertia degree, ramification index, discriminant, ramification polygon, and residual polynomials of the segments of…
We construct a topology on a given algebraically closed field with a distinguished subfield which is also algebraically closed. This topology is finer than Zariski topology and it captures the sets definable in the pair of algebraically…
The concern of this paper is to show that there always exist Krasner hyperfields of order n, where n is an integer greater than or equal to 2.
We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an extension.
There exist numerous results in the literature proving that within certain families of totally real number fields, the minimal rank of a universal quadratic lattice over such a field can be arbitrarily large. Kala introduced a technique of…
Dynkin's classification of maximal subalgebras of simple finite dimensional complex Lie algebras is generalized to Lie subsuperalgebras of the general linear Lie superalgebras.
In this short note we give some corollaries of the polynomial inverse function theorem for large fields. We prove inverse and implicit function theorems for Nash maps over large fields, characterize large fields as fields satisfying inverse…
A fully tensorial theoretical framework for hypercomplex-valued neural networks is presented. The proposed approach enables neural network architectures to operate on data defined over arbitrary finite-dimensional algebras. The central…
We prove that the main examples in the theory of algebraic differential equations possess a remarkable total differential overconvergence property. This allows one to consider solutions to these equations with coordinates in algebraically…
We establish the convergence theory of multiplicative Diophantine approximation for all non-degenerate, smooth manifolds. We also settle said convergence theory for all affine subspaces satisfying a highly generic and essentially optimal…
Given a field with a set of discrete valuations $V$, we show how the genus of a division algebra over the field is related to the genus of the residue algebras at various valuations in $V$ and the ramification data. When the division…
This is an introduction to the author theory of cyclic p-extensions of an absolutely unramified complete discrete valuation field K with arbitrary residue field of characteristic p. In this theory a homomorphism is constructed from the…
This article surveys results regarding the Tukey theory of ultrafilters on countable base sets. The driving forces for this investigation are Isbell's Problem and the question of how closely related the Rudin-Keisler and Tukey…
A Poisson geometry arising from maximal commutative subalgebras is studied. A spectral sequence convergent to Hochschild homology with coefficients in a bimodule is presented. It depends on the choice of a maximal commutative subalgebra…