9622750 Wadsworth This award supports the research of Professor A. Wadsworth to work in non-commutative ring theory with special emphasis on problems arising from the theory of central simple algebras with involutions. In particular, Professor Wadsworth will use the theory of index reduction to study the triality phenomena associated to algebras of degree 8. He will also study questions of when an orthogonal involution of an algebra becomes isotropic and the similarity between tensor products of quaternion algebras with involutions to Pfister quadratic forms. He also hopes to see if there are non twisted flag varieties for which index-reduction formulas hold. This is research in the subfield of algebra called non-commutative ring theory. Algebra can be thought of as the study of symmetry in the abstract. As such, algebra has direct applications to areas of physics and chemistry. In fact, much of non-commutative ring theory generalizes structures found in quantum mechanics.
