In this context, a natural question arises: is it possible to obtain such criteria for the Witt group of a central simple algebra with involution ?
Next, we consider the case of the Witt group of a quaternion division algebra endowed with its canonical involution.
3 The Witt group of a division algebra with involution
We refer to [13, Chapter 7,10] for more details about the Witt group.
The Witt group of (D,[sigma]) is the quotient group of the Grothendieck group of this commutative monoid by the subgroup generated by hyperbolic forms and is denoted by W (D,[sigma]).
In this Section, we prove isomorphy criteria for the Witt group of a quadratic field extension with its nontrivial automorphism and for the Witt group of a quaternion division algebra with its canonical involution, in analogy with Theorem 1.
CORDES: The Witt group and the equivalence of fields with respect to quadratic forms, J.