ALGEBRAS OF ODD DEGREE WITH INVOLUTION, TRACE FORMS AND DIHEDRAL EXTENSIONS

A 3-fold Pfister form is associated to every involution of the second kind on a central simple algebra of degree 3. This quadratic form is a ssociated to the restriction of the reduced trace quadratic form to th e space of symmetric elements; it is shown to classify involutions up to conjugation. Subfields with dihedral Galois group in central simple algebras of arbitrary odd degree with involution of the second kind a re investigated. A complete set of cohomological invariants for algebr as of degree 3 with involution of the second kind is given.