Mathematical Sciences: Central Simple Algebras with Involution

9622750沃兹沃斯奖支持A.Wadsworth教授致力于非对易环论的研究，特别强调了中心单代数与对合论所产生的问题。特别是，Wadsworth教授将使用指数归约理论来研究与8次代数有关的三次现象。他还将研究代数的正交对合何时变得各向同性以及对合为Pfister二次型的四元数代数的张量积之间的相似性问题。他还希望看看是否存在指数下调公式适用的非扭曲旗帜品种。这是代数子领域的研究，称为非对易环论。代数可以看作是对抽象对称性的研究。因此，代数在物理和化学领域有直接的应用。事实上，许多非对易环理论都概括了量子力学中的结构。

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.