Mathematical Sciences: Central Simple Algebras with Involution

9622750沃兹沃斯 该奖项支持了A教授的研究。沃兹沃斯工作的非交换环理论，特别强调的问题所产生的理论中心简单代数与对合。特别是，沃兹沃斯教授将使用指数约化理论来研究与8度代数相关的triality现象。他还将研究问题时，一个正交对合的代数成为各向同性和张量之间的产品的四元数代数与对合普菲斯特二次形式。他还希望看看是否有指数减少公式适用的非扭曲旗品种。 这是在代数的一个子领域的研究，叫做非交换环理论。代数可以被认为是抽象的对称性的研究。因此，代数直接应用于物理和化学领域。事实上，许多非对易环理论推广了量子力学中发现的结构。

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.