Mathematical Sciences: Minimal Embeddings in Central Simple Algebras

这个研究项目是关于环中的问题 理论和交易，更确切地说，与问题有关的 半单代数在中心单代数中的嵌入如果 A是一个半单K-代数，其中K是一个整体域，则 本研究的目标是确定最小尺寸 A嵌入的中心单K-代数的最小t 使得A嵌入到D上的t × t矩阵中，其中D是K- 分割环一个将被考虑的相关问题是， 确定给定群G的最小值t，使得t × t D上的矩阵是G的交叉积，对于某些K-除 环D. 本项目所支持的研究总体上是 环的理论。具体来说，首席研究员 将研究一个中心简单代数如何包含另一个。 这项工作借鉴了群论中的一些深入结果， 揭示了代数和数论中的各种问题。

This research project is concerned with problems in ring theory and deals, more precisely, with questions about the embedding of semi-simple algebras in central simple algebras. If A is a semi-simple K-algebra where K is a global field, then one goal of this investigation is to determine the minimum dimension of a central simple K-algebra in which A embeds and the minimum t such that A embeds in the t x t matrices over D, where D is a K- division ring. A related problem, which will be considered, is to determine for a given group G the minimum t such that the t x t matrices over D is a crossed product for G for some K-division ring D. The research supported in this project is in the general area of ring theory. Specifically, the principal investigator will study how one central simple algebra can contain another. This work draws on some deep results in group theory and will shed light on various questions in algebra and number theory.