Related papers: Free fields in skew fields

We discuss the decomposability of torsion-free abelian groups. We show that among computable groups of finite rank this property is $\Sigma^0_3$-complete. However, when we consider groups of infinite rank, it becomes $\Sigma^1_1$-complete,…

We extend discrete Morse-Bott theory to the setting of loop-free (or acyclic) categories. First of all, we state a homological version of Quillen's Theorem A in this context and introduce the notion of cellular categories. Second, we…

A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…

In this paper, we give a Gr\"obner-Shirshov basis of the free dendriform algebra as a quotient algebra of an $L$-algebra. As applications, we obtain a normal form of the free dendriform algebra. Moreover, Hilbert series and Gelfand-Kirillov…

We provide a characterisation of differentially large fields in arbitrary characteristic and a single derivation in the spirit of Blum axioms for differentially closed fields. In the case of characteristic zero, we use these axioms to…

Semi-free ideal rings, or semifirs, were introduced by Paul M. Cohn to study universal localizations in the non-commutative setting. We provide new examples of semifirs consisting of analytic functions in several non-commuting variables.…

We introduce the notion of pure Q-solvable algebra. The quantum matrices, quantum Weyl algebra, U_q(n) are the examples. It is proved that the skew field of fractions of pure Q-solvable algebra is isomorphic to the skew field of twisted…

We construct the universal central extension of the Lie algebra of exact divergence-free vector fields, proving a conjecture by Claude Roger from 1995. The proof relies on the analysis of a Leibniz algebra that underlies these vector…

In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we…

In this paper, we construct the associated vertex operator algebras for all $\mathcal{N}=2$ superconformal field theories of rank one. We give a uniform presentation through free-field realizations, which turns out to be a particularly…

Subtraction-free computational complexity is the version of arithmetic circuit complexity that allows only three operations: addition, multiplication, and division. We use cluster transformations to design efficient subtraction-free…

We present two constructions of projective systems of measures associated to discretizations of free scalar Euclidean quantum fields. The first one is obtained using only purely combinatorial data and applies to free massless scalar fields…

We study (relative) K-Mittag-Leffler modules, with emphasis on the class K of absolutely pure modules. A final goal is to describe the K-Mittag-Leffler abelian groups as those that are, modulo their torsion part, aleph_1-free, Cor.6.12.…

In this paper, by assuming a faithful action of a finite flat $\mathbb{Z}_p$-algebra $\mathscr{R}$ on a $p$-divisible group $\mathcal{G}$ defined over the ring of $p$-adic integers $\mathscr{O}_K$, we construct a category of new…

In the TQFT formalism of Moore-Tachikawa for describing Higgs branches of theories of class $\mathcal{S}$, the space associated to the unpunctured sphere in type $\mathfrak{g}$ is the universal centraliser $\mathfrak{Z}_G$, where…

We describe relations between maximal subfields in a division ring and in its rational extensions. More precisely, we prove that properties such as being Galois or purely inseparable over the centre generically carry over from one to…

We determine the possible Hilbert functions of graded rank one torsion free modules over three dimensional Artin-Schelter regular algebras. It turns out that, as in the commutative case, they are related to Castelnuovo functions. From this…

For a torsion free finitely generated nilpotent group G we naturally associate four finite dimensional nilpotent Lie algebras over a field of characteristic zero. We show that if G is a relatively free group of some variery of nilpotent…

In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for $L$-functions. Our results generalize and improve previous results obtained by N. Nikolski and…

Although in general there is no meaningful concept of factorization in fields, that in free associative algebras (over a commutative field) can be extended to their respective free field (universal field of fractions) on the level of…