On the decomposition of quadratic pairs in characteristic two

In this paper, we study the decomposition of central simple algebras of low degrees with quadratic pair in characteristic two. For algebras of degree [Formula: see text], a decomposition criterion is obtained in terms of square-central elements. Also, using square-central and Artin–Schreier elements, all possible decompositions of an algebra of degree 8 with quadratic pair are studied. This includes the decomposition into an invariant subalgebra of degree 2 or 4 with quadratic pair and its centralizer, in both cases where the restriction of the involution to the centralizer is either symplectic or orthogonal.