Mathematical Sciences: Minimal Embeddings in Central Simple Algebras

点击翻译按钮获取中文摘要

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.