Related papers: Galois actions by finite quantum groupoids

We introduce Galois Theory for Hopf-Galois Extensions proving existence of a Galois connection between subalgebras of an H-comodule algebra and generalised quotients of the Hopf algebra H. Moreover, we show that these quotients Q which…

We present a Galois theory connecting finitary operations with pairs of finitary relations one of which is contained in the other. The Galois closed sets on both sides are characterised as locally closed subuniverses of the full iterative…

In 2020, Alabdali and Byott described the Hopf-Galois structures arising on Galois field extensions of squarefree degree. Extending to squarefree separable, but not necessarily normal, extensions $L/K$ is a natural next step. One must…

For an algebraically closed field K, let G be a finite abelian group of K-linear automorphisms of a finite-dimensional path algebra KQ of a quiver Q. Under certain assumptions on the action of G, we show the existence of a certain kind of…

The aim of this paper is to extend our old results about Galois action on the torsion points of abelian varieties to the case of (finitely generated) fields of characteristic 2.

Let $H$ be a finite-dimensional weak Hopf algebra over a field $k$ and $A/B$ be a right faithfully flat weak $H$-Galois extension. We prove that if the finitistic dimension of $B$ is finite, then it is less than or equal to that of $A$.…

In this paper, our objects of interest are Hopf Galois extensions (e.g., Hopf algebras, Galois field extensions, strongly graded algebras, crossed products, principal bundles, etc.) and families of noncommutative rings (e.g., skew…

We establish the faithfulness of a geometric action of the absolute Galois group of the rationals that can be defined on the discriminantal variety associated to a finite complex reflection group, and review some possible connections with…

We review the depth two and Hopf algebroid-Galois theory in math.RA/0108067 and specialize to induced representations of semisimple algebras and character theory of finite groups. We show that depth two subgroups over the complex numbers…

We classify Galois objects for the dual of a group algebra of a finite group over an arbitrary field.

This article develops the theory of fusion categories acting on algebras. We will demonstrate that weak Hopf algebra actions on algebras correspond to specific actions of fusion categories. As an application of this theory, we introduce a…

We study the Ehresmann--Schauenburg bialgebroid of a noncommutative principal bundle as a quantization of the gauge groupoid of a classical principal bundle. We show that the gauge group of the noncommutative bundle is isomorphic to the…

An extension B\subset A of algebras over a commutative ring k is an H-extension for an L-bialgebroid H if A is an H-comodule algebra and B is the subalgebra of its coinvariants. It is H-Galois if the canonical map A\otimes_B A\to A\otimes_L…

By using the language of cogroupoids, we show that Hopf-Galois objects of a twisted Calabi-Yau Hopf algebra with bijective antipode are still twisted Calabi-Yau, and give their Nakayama automorphism explicitly. As applications, cleft Galois…

We consider endomorphism actions of arbitrary discrete semigroups on a connected metrizable topological group G. We give necessary and sufficient conditions for expansiveness of such actions when G is a Lie group or a compact…

The notion of a coalgebra-Galois extension is defined as a natural generalisation of a Hopf-Galois extension. It is shown that any coalgebra-Galois extension induces a unique entwining map $\psi$ compatible with the right coaction. For the…

We investigate the transformed Hopf algebras in Hopf Galois extensions. The final goal of this paper is to introduce certain triangular Hopf algebras associated with restricted Frobenius Lie algebras over a field of characteristic $p>0$.

Mimicking a recent article of Stefaan Vaes, in which was proved that every locally compact quantum group can act outerly, we prove that we get the same result for measured quantum groupoids, with an appropriate definition of outer actions…

A coaction of a Hopf algebra on a unital algebra is called homogeneous if the algebra of coinvariants equals the ground field. A coaction of a Hopf algebra on a (not necessarily unital) algebra is called Galois, or principal, or free, if…

In a previous work, the second-named author gave a complete description of the action of automorphisms on the ordinary irreducible characters of the finite symplectic groups. We generalise this in two directions. Firstly, using work of the…