Hasse invariant of a quadratic form
- Hasse invariant of a quadratic form
In mathematics, the Hasse invariant (or Hasse-Witt invariant) of a quadratic form "Q" over a field "K" takes values in the Brauer group Br("K").The quadratic form "Q" may be taken as a diagonal form
:Σ "a""i""x""i"2.
Its invariant is then defined as the sum of the classes in the Brauer group of all the quaternion algebras
:("a""i", "a""j") for "i" < "j".
It may also be viewed as the second Stiefel-Whitney class of Q.
The name "Hasse-Witt" comes from Helmut Hasse and Ernst Witt.
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