Related papers: Galois groups of the basic hypergeometric equation…
This paper is concerned with difference equations on elliptic curves. We establish some general properties of the difference Galois groups of equations of order two, and give applications to the calculation of some difference Galois groups.…
We introduce a generalisation of norm relations in the group algebra Q[G], where G is a finite group. We give some properties of these relations, and use them to obtain relations between the S-unit groups of different subfields of the same…
The main motivation of our work is to create an efficient algorithm that decides hypertranscendence of solutions of linear differential equations, via the parameterized differential and Galois theories. To achieve this, we expand the…
We present a geometric setting for the differential Galois theory of $G$-invariant connections with parameters. As an application of some classical results on differential algebraic groups and Lie algebra bundles, we see that the Galois…
We present a simple method for the construction of polynomials with cyclic Galois groups, hoping to encourage a reader with some background in algebra to make computations of his/her own.
In this paper we will give the calculus, the criterion, and the existence of the arithmetic Galois covers of higher relative dimensions.
We report on an implementation of Galois groups in the new computer algebra system OSCAR. As an application we compute Galois groups of Ehrhart polynomials of lattice polytope
We give the hypergeometric solutions of some algebraic equations including the general fifth degree equation.
In this work we carry out a complete group classification of Burgers' equations.
Let G be a linear algebraic group, not necessarily connected or reductive, over the field of real numbers R. We describe a method, implemented on computer, to find the first Galois cohomology set H^1(R,G). The output is a list of 1-cocycles…
We define the fundamental group of a Hopf algebra over a field. For this purpose we first consider gradings of Hopf algebras and Galois coverings. The latter are given by linear categories with new additional structure which we call Hopf…
Let G be a connected, compact, semisimple algebraic group over the field of real numbers R. Using Kac diagrams, we describe combinatorially the first Galois cohomology sets H^1(R,H) for all inner forms H of G. As examples, we compute…
We compute the fundamental group of the Galois cover of a surface of degree~$8$, with singularities of degree $4$, whose degeneration envelope is isomorphic to an octahedron. The group is shown to be a metabelian group of order $2^{23}$.…
We study the Galois groups of polynomials arising from a compatible family of representations with big orthogonal monodromy. We show that the Galois groups are usually as large as possible given the constraints imposed on them by a…
We introduce an abstract topos-theoretic framework for building Galois-type theories in a variety of different mathematical contexts; such theories are obtained from representations of certain atomic two-valued toposes as toposes of…
We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.
We compute the Picard group of the moduli stack of stable hyperelliptic curves of any genus, exhibiting explicit and geometrically meaningful generators and relations.
We explain in detail the definition, construction and generalisation of the Galois group of Chebyshev polynomials of high degree to the Galois group of chaotic chains. The calculations in this paper are performed for Chebyshev polynomials…
In this article we present a new method to obtain polynomial lower bounds for Galois orbits of torsion points of one dimensional group varieties.
In this paper, we explain how to compute the Lie algebra of the differential Galois group of a reducible linear differential system. We achieve this by showing how to transform a block-triangular linear differential system into a…