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。本研究分为两部分。一是研究大于2维的局部Brauer群，二是将Brauer群中的类显式地表示为循环代数的乘积。支持的研究是在一般领域的场论。域是类似于有理数、实数和复数的代数结构，因为每个非零元素相对于乘法有一个逆。场论是一门丰富而深刻的学科，其历史根源源于早期系统地描述多项式零点的尝试。

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.