Extensions galoisiennes non commutatives :normalité cohomologie non abélienne

Abstract

We study various types of noncommutative Galois extensions and present some examples. We state a criterion which decides whether a given automorphism of a Galois extension belongs to the corresponding Galois group or not. We then compute Borovoi’s nonabelian cohomology sets (in degree 0, 1, 2) of the Galois group with coefficients in a crossed module associated to the Galois extension.

Keywords:

• Galois-extension
• non-commutative ring
• idempotent
• quaternion
• crossed-module
• non abelian cohomology

Mathematics Subject Classification (1991):

• 16W20
• 16H05
• 16K20
• 18G50
• 08A35