Mathematical Sciences: Quadratic Regular Algebras

该奖项支持M教授的研究。Vancliff的工作在非交换环理论，特别强调问题所产生的理论分级经常代数。特别是，Vancliff教授将尝试分类的二次正则代数的整体维数n希尔伯特级数相同的多项式环上的n个变量，映射到一定的扭曲齐次坐标环的一个二次躺在n-1维射影空间。她希望这将导致方法的建设的例子阿廷Schelter代数与新的行为。 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，大部分非对易环理论概括了量子力学中发现的结构，并且该提议继续探索与现代量子场论直接相关的领域。

This award supports the research of Professor M. Vancliff to work in non-commutative ring theory with special emphasis on problems arising from the theory of graded regular algebras. In particular, Professor Vancliff will try to classify the quadratic regular algebras of global dimension n with Hilbert series the same as that of the polynomial ring on n variables that map onto a certain twisted homogeneous coordinate ring of a quadric lying in n-1 dimensional projective space. She hopes that this will lead to methods of constructing examples of Artin-Schelter algebras with new behavior. 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 and this proposal continues to explore areas that connect directly with modern quantum field theory.