A Galois theory for finite factors

Harmonic Galois theory for finite graphs

This paper develops a harmonic Galois theory for finite graphs, thereby classifying harmonic branched G-covers of a fixed base X in terms of homomorphisms from a suitable fundamental group of X together with G-inertia structures on X. As applications, we show that finite embedding problems for graphs have proper solutions and prove a Grunwald-Wang type result stating that an arbitrary collectio...

Galois Theory for Beginners

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Galois Theory

Galois Theory

Remark 0.1 (Notation). |G| denotes the order of a finite group G. [E : F ] denotes the degree of a field extension E/F. We write H ≤ G to mean that H is a subgroup of G, and N G to mean that N is a normal subgroup of G. If E/F and K/F are two field extensions, then when we say that K/F is contained in E/F , we mean via a homomorphism that fixes F. We assume the following basic facts in this set...

A Note on Galois Theory for Bialgebroids

In this note we reduce certain proofs in [9, 5, 6] to depth two quasibases from one side only. This minimalistic approach leads to a characterization of Galois extensions for finite projective bialgebroids without the Frobenius extension property: a proper algebra extension is a left T -Galois extension for some right finite projective left bialgebroid T over some algebra R if and only if it is...