Mathematical Sciences: Minimal Embeddings in Central Simple Algebras

本课题主要研究中心单代数的结构以及它们组合成Brauer群的方式。主要研究人员将研究中心单代数，以探索它们中的一个如何包含另一个。一个最终的目标是探索如何将由中心单代数建立的半单代数插入到其他域上的中心单代数中。这些问题的解将在有限群论中得到应用。研究支持了一个领域的布劳尔小组的研究。这个群是一个不变量，它帮助解释作为矩阵环或线性变换的子代数出现的域上的代数的结构。这项工作揭示了有限维除环的结构，并对有限群论有潜在的应用。

This project is concerned with the structure of central simple algebras and the ways in which they combine to form Brauer groups. The principal investigator will study central simple algebras in order to explore how one of them can contain another. An ultimate goal is to explore how semisimple algebras, which are built from central simple algebras, can be inserted into central simple algebras over other fields. Solutions to these problems will have applications in the theory of finite groups. The research supported concerns the study of the Brauer group of a field. This group is an invariant that helps to explain the structure of the algebras over fields that occur as subalgebras of rings of matrices or linear transformations. This work has shed light on the structure of finite dimensional division rings and has potential applications to the theory of finite groups.