MA 764, Spring 2026: Hopf Algebras

1. Monday, January 12: Associative Algebras

2. Wednesday, January 14: Graded algebras; Co-algebras

3. Friday, January 16: More co-algebra examples; Sweedler notation

4. Wednesday, January 21: Duals of algebras and co-algebras

5. Friday, January 23: More duals

Monday, January 26: NO CLASS, SNOW DAY

Wednesday, January 28: NO CLASS, SNOW DAY

6. Friday, January 30: More coalgebra language

7. Monday, February 2: Bialgebras

8. Wednesday, February 4: Antipodes and Hopf algebras

9. Friday, February 6: Properties of Antipodes

10. Monday, February 9: Antipode examples

11. Wednesday, February 11: Finding antipodes

12. Friday, February 13: Hopf maps and Hopf duals

13. Monday, February 16: Modules & Comodules

14. Wednesday, February 18: Hopf modules

    • Main sources: [Mon93, Ch. 1] and [Rad12, Ch. 8]

    • Outline due 8pm

    • CELT visit to class

15. Friday, February 20: Hopf modules, continued (same notes as above)

16. Monday, February 23: Finish Hopf modules; start graded Lie algebras

    • Main sources: [MP12, Ch. 22] and [MM65, Section 5]

    • See also [Reu01]

17. Wednesday, February 25: Universal Enveloping Algebras

18. Friday, February 27: Poincare-Birkhoff-Witt

19. Monday, March 2: Primitives of Universal Enveloping Algebras

    • See [Car06] Section 3.6

20. Wednesday, March 4: prim U(L) = L

    • See [MM65]

21. Friday, March 6: Coradical filtrations (continued from last time)

22. Monday, March 9: gr H is (graded) commutative

23. Wednesday, March 11: primitive generation

24. Friday, March 13: Wrap up the proof of Milnor Moore

Spring break: No class March 16, 18, 20

25. Monday, March 23: The Hopf algebra of symmetric functions

    • See [GR14]

26. 
    

• Updates to final assignment (20 Feb)

  • Paper must be less than or equal to 15 pages

  • Presentation must be less than or equal to 20 minutes

• Course Information Sheet

• Final Project Information

• Paper Prospectus: due 8pm EST on Wednesday, January 28

• Paper outline: due 8pm on Wednesday, February 18 (updated)

• Draft Assignments

  • Draft 1 check-in: due Friday, March 13

    • It is ok if you are not done yet. Turn in whatever you have so far, and make a note of questions you have for me or challenges you are facing.

  • Draft 2: due Friday, April 3

    • This should be a polished draft ready to be read by your peers.

• Peer feedback assignment: due Monday, April 13

• Final paper & presentation

  • Presentations begin: Wednesday, 22 April

  • Final paper: due Monday, May 4

• TENTATIVE FINAL PRESENTATION SCHEDULE

  • Wednesday, 22 April: Usman, Blake

  • Friday, 24 April: Evan, Vinayak

  • Monday, 27 April: Max, Lok

  • Wednesday, 29 April: Prerna + backup slot