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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


Michael Taylor
UNC Chapel Hill
MR ID: 210423
Reference #


Posted date
2021-06-26 05:43:03
Revised date
2021-06-27 17:08:02
Notes type
   Standard Course Offering
   Topics Course
      Linear Algebra
      Group Theory
      Lie Algebras
      Harmonic Analysis
      Functional Analysis
      Differential Geometry
   Representation Theory

Introduction to Lie Groups

This set of notes on Lie groups is an update of my "Lectures on Lie Groups." The current version is now organized into chapters, the first 7 of which cover the original material, from a first look at Lie groups through basic material on representations of compact groups, with emphasis on the unitary, orthogonal and spin groups. New chapters make contact with harmonic analysis. The final chapter introduces G2. Appendices provide background and complementary results.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v1 PDF (1.8M) 06/26/21