arXiv 0901.08272009-01math.RTmath.RA

表示论导论

Introduction to representation theory

Pavel Etingof, Oleg Golberg, Sebastian Hensel, Tiankai Liu, Alex Schwendner, Dmitry Vaintrob, Elena Yudovina

备注：: 108 pages. In the latest version, misprints and errors were corrected and new exercises were added, in particular ones suggested by Darij Grinberg

摘要：

这些是课堂讲稿，产生于表示论课程的第一作者给其余六位作者在2004年3月的框架内克莱数学研究所研究学院的高中生，其扩展版本的第一作者给麻省理工学院本科数学学生在2008年秋季。这些笔记涵盖了一些标准的主题，在表示论的团体，李代数，和箭袋，并包含许多问题和练习。他们应该是访问的学生在线性代数和抽象代数的基础知识有很强的背景，并可用于本科或介绍研究生课程的表示论。

英文摘要：

These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students, and its extended version given by the first author to MIT undergraduate math students in the Fall of 2008. The notes cover a number of standard topics in representation theory of groups, Lie algebras, and quivers, and contain many problems and exercises. They should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra, and may be used for an undergraduate or introductory graduate course in representation theory.

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。