PMATH 863Introduction to Lie Groups and Lie Algebras
- Units
- 0.50
- Level
- Graduate
- Faculty
- Mathematics
- Subject
- Pure Mathematics
When it runs
- F24
- W25
- S25
- F25
- W26
- S26
- F26
- W27
- S27
Ran in 2 of the last 7 terms. Winter 2027: scheduled, 1 lecture section. Spring 2027: schedule not out yet.
An introduction to matrix Lie groups and their associated Lie algebras: geometry of matrix Lie groups; relations between a matrix Lie group and its Lie algebra; representation theory of matrix Lie groups.
Prerequisites
None listed.
Antirequisites
None listed.
Leads to
No course lists it as a requisite.
Winter 2027 sections
| Section | Class | Enrolled | Meets |
|---|---|---|---|
| LEC 001 | 7449 | 0 / 30 | MWF 10:30–11:20 |
Reviewed on UW Flow
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From 1 rating and 1 comment on UW Flow. The most helpful comments, quoted as written, without names. Read them all on UW Flow.
Amazing subject, though the course itself feels weirdly designed in terms of prerequisites - one could easily suppose slightly more analysis, algebra, or geometry to be able to cover substantially more material. Our course was split roughly into thirds: the basic definitions and examples of (matrix) Lie groups and Lie algebras, structure theory of Lie algebras, and representation theory of compact (matrix) Lie groups, ending with a discussion (but nowhere close to a full coverage) of the techniques that go into classifying compact Lie groups with roots, weights, and their combinatorial friends. Because of how little we assumed at the start (really, you could take this course with just Math…
Apr 2026 · liked itOn UW FlowRemove this
Discussed on r/uwaterloo
4 posts and comments in 4 threads mention PMATH 863, November 2018 to December 2024. Quoted word for word, newest first; each reply sits under the post and the comment that started its branch. Search r/uwaterloo for newer posts.
Fall 2022
AMA - your academic advisor is here 35 points, 21 comments
“Title.”
u/uw_academic_advisor: “That guy is a phony”
u/Careless-Cow-5683: “pmath 863 - intro to lie groups and lie algebras”
Spring 2022
Mathematical physics Course blueprint recommendations 3 points, 21 comments
“Hey everyone, I’m going into the mathematical physics program at Waterloo next year and I was wondering if anyone had any recommendations on a sort of blueprint I could follow for courses because …”
u/Yu-Li: “… PHYS 475 (get override request) / PHYS 468 Change coop sequence 4A winter: AMATH 474 PMATH 863 AMATH 475 PHYS 359 One more physics course you like (I would choose from quantum computing/ continuum mechanics/ computational physics) Then do more research coop terms and study terms …”
Fall 2018
Bird Courses for Winter 2019 8 points, 6 comments
“Any suggestions for easy bird courses during Winter 2019?”
u/mathlord1337: “PMATH 810, 863, 940, 945, 950, 964”
Math Faculty 1 point, 7 comments
u/spectral_theorem: “… e.g., next term there's Lie groups/algebras, C-algebras, and some differential geometry (PMATH 863, 950, 965) I guess a concrete benefit of having a math faculty is that some profs may be into that sort of thing at an admin level; as a consequence a lot of the math profs you'll …”
Check it elsewhere for Fall 2026
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