Teichmüller cocycle

In mathematics, the Teichmüller cocycle is a certain 3-cocycle associated to a simple algebra A over a field L which is a finite Galois extension of a field K and which has the property that any automorphism of L over K extends to an automorphism of A. The Teichmüller cocycle, or rather its cohomology class, is the obstruction to the algebra A coming from a simple algebra over K. It was introduced by Teichmüller and named by Eilenberg and MacLane.

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