局部Moufang集
Local Moufang sets
摘要：
所有已知的牟方集都以某种方式产生于一种代数结构，这种代数结构在某种程度上可以称为“除法”。在这篇博士论文中，我试图发展一个局部Moufang集的理论，它以一种允许使用相应的局部代数结构来构造的方式来推广Moufang集。本文分为两大部分，第一部分是对局部Moufang集理论的发展，第二部分是构造一些实例。最一般的例子是从一个局部的约当对（对应于一个局部的约当代数）中构造出来的，其中一个主要定理刻画了这些局部的Moufang集。
英文摘要：
All known Moufang sets arise, in some way or another, from an algebraic structure which can be called `division' in some way. In this PhD dissertation, I made an attempt to develop a theory of local Moufang sets, which generalize Moufang sets in a way to allow constructing using the corresponding local algebraic structures. In the first of the two major parts of the dissertation, I develop the theory of local Moufang sets, while in the second part, some examples are constructed. The most general example constructed arises from a local Jordan pair (which corresponds to a local Jordan algebra), and one of the main theorems characterizes these local Moufang sets.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
