Mathematical Sciences: Crossed Products over Rational Function Fields

本课题主要研究除环、中心单代数的结构，以及它们组合成Brauer群的方法。利用有限群，可以将除环描述为交叉积。一个最终目标是将群的结构与环中心的算术性质联系起来。所支持的研究是在环理论的一般领域。环是定义了加法和乘法的代数对象。环在数学的许多领域中都是自然存在的。这位首席研究员将研究一个环如何包含另一个环。这项工作借鉴了群论中的一些深刻结果，并将有助于揭示代数和数论中的各种问题。

This project is concerned with the structure of division rings, central simple algebras, and the ways in which they combine to form Brauer groups. Using finite groups, it is possible to describe division rings as crossed products. An ultimate goal is to relate the structure of the group with the arithmetic properties of the center of the ring. The research supported is in the general area of ring theory. A ring is an algebraic object having an addition and a multiplication defined on it. Rings occur naturally in many areas of mathematics. This principal investigator will study how one ring can contain another. The work draws on some deep results in group theory and will shed light on various questions in algebra and number theory.