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Forms of Hopf algebras and Galois theory. (English) Zbl 0724.16019

Topics in algebra. Pt. 1: Rings and representations of algebras, Pap. 31st Semester Class. Algebraic Struct., Warsaw/Poland 1988, Banach Cent. Publ. 26, Part 1, 75-93 (1990).
[For the entire collection see Zbl 0716.00006.]
The author first surveys the present state of the theory of forms of Hopf algebras and of Hopf Galois theory, especially for separable extensions. Then he gives some new or partial results, for example characterizing an F-Galois extension K/k of a field k for a finite group F, and characterizing separable field extensions K/k of prime degree which are Hopf Galois. Some open questions are mentioned.

MSC:

16W30 Hopf algebras (associative rings and algebras) (MSC2000)
12F10 Separable extensions, Galois theory
16W20 Automorphisms and endomorphisms

Citations:

Zbl 0716.00006