Fundamental concepts in non-commutative algebra, Math 80598

Announcements:

March 19. I reserved room 70 in Ross for our meetings on Tuesdays at 10:00-11:45. This will be instead of Sunday lectures.
March 11. Here are Lior's notes of the first and second recitations.
March 4. To get a general idea of what the course is about you can look at this link to an analogous webpage of a math598 course I gave a year ago. Needless to say, this time some things may go differently, so the link is for a general impression only.

General Info:

Instructor:

· Michael Temkin

· E-mail: temkin $http://www.math.huji.ac.il/~temkin/images/at.gif$ math.huji.ac.il

· Office: Ross 78A (tel. 02-6584575)

· Office Hours: by appointment

· Lectures: Sundays 9-10:45 at Shprintzak 27, Wednesdays 10-12:45 at Shprintzak 201.

Teaching Assistants:

· Lior Yanovsky

· E-mail: lior.yanovski $http://www.math.huji.ac.il/~temkin/images/at.gif$ gmail.com

· Office:

· Office Hours: by appointment

· Recitations: Sundays 12-13:45 at Sprintzak 28.

Texts:

· We will mainly use "Non-commutative Algebra" by Farb and Dennis, but a few complements may be from other sources.

Grading:

· The final grade will be obtained as follows: 80% of the exam grade plus 20% of the homework grade. The grade for homework will be computed by averaging 10 best weekly homework grades.

Homework:

· The exercises are assigned on Wednesdays on this webpage, and should be submitted to Lior on recitation in ten days (or earlier to his mailbox). Late (or non-submitted) homework will not be graded. You may discuss the problems or cooperate when thinking about them, but each student should write his solution separately. Some homework may have non-mandatory part that will not affect the grading; you are advised to work on it if you want to study the course topic deeper.

Homework Assignments:

More difficult problems are marked with *.

March 4. The first homework is here. The due date is March 15.
March 11. The second homework is here. The due date is March 22.
March 18. The third homework is here. The due date is April 12.
April 16. The fourth homework is here. The due date is April 23.

Lectures:

March 1. Half of chapter 0. Non-commutative rings, ideals (left, right and two-sided), left (or right) modules, the opposite ring, R-S-bimodules, the group H=Hom_R(M,N) and the ring End_R(M), the S-module structure on H when M or N is an R-S-bimodule.
March 4. The rest of chapter 0. Group rings and monoid rings. Tensor products of modules, bimodules and algebras.
March 8. Repetition o the material.
March 11. Simple and semi-simple modules.
March 15. Automorphisms of semisimple modules, semisimple rings and Wedderburn's theorem.
March 18. Simple artinian rings: properties and classification.
April 14. Representations of finite groups: the ring k[G] and two bases of its center.
April 15. Characters and the orthogonality relations, table of characters of a group.
April 21. Brauer's p^aq^b theorem.
April 22. Induction and Frobenius reciprocity.
April 29. Jacobson radical, Lemma of Nakayama.
April 30. Hopkins theorem and the rest of chapter 2.
May 5. Representations of GL_2(F_q).
May 6. Representations of S_n.