Related papers: Rigid Real Closed Fields

We show that there exist closed manifolds with arbitrarily small transcendental simplicial volumes. Moreover, we exhibit an explicit uncountable family of (transcendental) real numbers that are not realised as the simplicial volume of a…

A new class of infinite dimensional simple Lie algebras over a field with characteristic 0 are constructed. These are examples of non-graded Lie algebras. The isomorphism classes of these Lie algebras are determined. The structure space of…

Vacuum gravitational fields invariant for a bidimensional non Abelian Lie algebra of Killing fields, are explicitly described. They are parameterized either by solutions of a transcendental equation (the tortoise equation) or by solutions…

Admitting non-Riemannian geometries, Double Field Theory extends the notion of spacetime beyond the Riemannian paradigm. We identify a class of singular spacetimes known in General Relativity with regular non-Riemannian geometries. The…

In this short article accessible for non-experts I discuss possible ways of constructing a non-commutative gravity paying special attention to possibilities of realizing the full diffeomorphism symmetry and to relations with 2D gravities.

The space $SL(2,\mathbb{R})\times SL(2,\mathbb{R})$ admits a natural homogeneous pseudo-Riemannian nearly Kaehler structure. We investigate almost complex surfaces in this space. In particular we obtain a complete classification of the…

This paper shows that in general, difference fields do not have a difference closure. However, we introduce a stronger notion of closure (kappa-closure), and show that every algebraically closed difference field K of characteristic 0, with…

We construct a nil algebra over a countable field which has finite but non-zero Gelfand-Kirillov dimension.

We construct a non-Abelian gauge theory of chiral 2-forms (self-dual gauge fields) in 6 dimensions with a spatial direction compactified on a circle of radius R. It has the following two properties. (1) It reduces to the Yang-Mills theory…

We introduce a graded version of dagger closure and prove that it coincides with solid closure for homogeneous ideals in two dimensional $\mathbb{N}$-graded domains of finite type over a field.

This paper reproduces the text of a part of the Author's DPhil thesis. It gives a proof of the classification of non-trivial, finite homogeneous geometries of sufficiently high dimension which does not depend on the classification of the…

The aim of this work is the study of left-invariant magnetic fields on 2-step nilpotent Lie groups. While the existence of closed 2-forms for which the center is either nondegenerate or in the kernel of the 2-form, is always guaranteed, the…

In this investigation, we introduce the class of non-archimedean frames in spirit with the topological notion of non-archimedean spaces. We explore various properties of these frames - particularly their spaciality. We attach a base that…

We construct the first sharply $3$-transitive groups not arising from a near field, i.e. point stabilizers have no nontrivial abelian normal subgroup.

We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo-finite fields over A. Assuming GCH, we generalise this result to \kappa-prime models, for \kappa a regular uncountable cardinal or…

We study non-Abelian fields in the context of very special relativity (VSR). For this we define the covariant derivative and the gauge field gauge transformations, both of them involving a fixed null vector $n_{\mu}$, related to the VSR…

We characterize finite-dimensional Lie algebras over an arbitrary field of characteristic zero which admit a non-trivial (quasi-) triangular Lie bialgebra structure.

We consider finite extensions of the rationals which are unramified except for at 2 and infinity. We show there are no such extensions of degrees 9 through 15.

Let $K$ be a Henselian, non-trivially valued field with separated analytic structure. We prove the existence of definable retractions onto an arbitrary closed definable subset of $K^{n}$. Hence directly follow definable non-Archimedean…

We construct a faithfully flat algebra over the infinite polynomial ring on an algebraically closed field that is not descendable.