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Open Math Notes

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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto

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Michael Taylor
UNC Chapel Hill
MR ID: 210423
Reference #
OMN:202106.111301

Attributes

Posted date
2021-06-26 05:43:03
Revised date
2023-07-06 09:01:45
Level
   Graduate
Notes type
   Standard Course Offering
   Topics Course
Topic
   Algebra
      Linear Algebra
      Group Theory
      Lie Algebras
   Analysis
      Harmonic Analysis
      Functional Analysis
   Geometry
      Differential Geometry
   Representation Theory

Introduction to Lie Groups

These notes treat basic Lie group theory, starting with definitions and basic examples. They proceed to bring in the group integral and Lie algebra, and use these concepts to develop basic results on representation theory, with an emphasis on compact groups. The text alternates between treatments of general results and specific cases, such as unitary groups, orthogonal groups and related spin groups, and quaternionic unitary groups. The final chapter introduces the exceptional group G2.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v2 PDF (2.3M) 07/06/23