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Unitary involutions on a simple central algebra after a scalar extension

Then we know that there exist unitary $L/K$-involutions on $A$ (i.e. involutions of the second kind leaving $K$ element-wise invariant). … In "The Book of Involutions" by Knus, Merkurjev, Rost and Tignol, I found (3.17) and (3.19) giving a correspondence between unitary $L/K$-involutions on $A$ and the right ideals $I\subset N_{L/K}(A)$ …