Hasse invariant of a quadratic form

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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_ix_i².

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.