Discriminant algebras and adjoints of quadratic forms (Q1356594)

The discriminant algebra of a nonsingular quadratic form \(q\) is defined as the centralizer of the even Clifford algebra in the full Clifford algebra. The author presents a definition of the discriminant algebra of a possibly quadratic form which avoids the Clifford algebra. The half- and the quarter-determinant, an Amitsur 1-cocycle, exterior and Pfaffian powers of bilinear forms are just a few of the tools used in the process.