Mathematical Sciences: Division Algebras, Brauer Groups, andField Theory

这个项目涉及除法代数、布劳尔群和场论的研究。这项研究分为两个部分。第一种是研究维度大于2的局部Brauer群，第二种是将Brauer群中的一类显式地表示为循环代数的乘积。所支持的研究属于场论的一般领域。域是类似于有理数、实数和复数的代数结构，因为每个非零元素都有一个关于乘法的逆。场论是一门丰富而深刻的学科，它的历史根源源于早期系统地描述多项式的零点的尝试。

This project concerns research on division algebras, Brauer groups, and field theory. There are two parts to the research. The first is to study local Brauer groups in dimensions greater than two, and the second is to express a class in the Brauer group as a product of cyclic algebras in an explicit way. The research supported is in the general area of field theory. Fields are algebraic structures similar to the rational numbers, the real numbers, and the complex numbers in that each nonzero element has an inverse with respect to multiplication. Field theory is a rich and deep subject with its historical roots arising from the early attempts to systematically describe the zeros of polynomials.