Messages
08.05: Error in Lecture notes 5. On the first page (Exercise 1 and 2), please ignore what is in the parenthesis on the first line, it is not correct. Please also ignore the comment just below that parenthesis, since it is irrelevant and confusing. (Thanks to Ulrik, for pointing it out!)
23.04: The lecture Thursday April 24, 16.15-18.00 will be in room 656, 6th floor Sentralbygg II.
07.04: The lecture today, April 7, 15.15-17.00 will be in room R4 (until 16.00) and R9 (the second half).
03.04: The lecture today, April 3, 16.15-18.00 will be in room 656, 6th floor Sentralbygg II.
26.03: On Monday 7.4, the lecture will be one hour later than usual, that is 15.15-17.00. And it will be in romm 822 in Sentralbygg II.
03.02: There will be no lectures March 14,17,21,24. There will be additional lectures on Thursday April 3 and April 24,at 16.15-18.00
14.02: On Monday 17.2, the lecture will be one hour later than usual, that is 15.15-17.00. And it will be in R3, in Realfagsbygget.
24.01: There will be no lecture on Monday 27.1.
09.01: The second lecture will be on Monday 13.1.Time: 14-15-16.00 We have a new schedule and new rooms from next week. See below.
08.01: I have added this book Assem-Coelho: Basic Representation Theory of Algebras to the literature list. It is digitally available for free (when logged in via NTNU).
The first meeting is scheduled for Wednesday, January 8th, at 12.15 in
The first meeting is scheduled for Thursday, January 9th, at 08.15 in R57
If you plan to or are considering following the course, please e-mail me at aslak [dot] buan [at] ntnu [dot] no if you cannot come to the first meeting.
Lecturer
Aslak Bakke Buan, room 846, Sentralbygg II, aslak [dot] buan [at] ntnu [dot] no
Schedule
Lectures are scheduled to
Wednesdays from 12:15 to 14:00, and
Thursdays from 08:15 to 10:00.
and will be in R57 (in "Realfagsbygget").
Mondays from 14:15 to 16:00 (in R4 in Realfagsbygget map) , and Fridays from 10:15 to 12:00 (in KJL22 in Kjelhuset map), with the following exceptions:
Monday 17.02: from 14:15 to 16:00 (in R3 in Realfagsbygget)
Friday 14.02: in KJL24 (in Kjelhuset)
Friday 10.01, Friday 14.03, Monday 17.03, Friday 21.03: NO LECTURE
The last lecture will most probably be on Monday 28.04
Exercises
There will be exercises roughly every second week. These will appear here and also be announced during lectures, and we will discuss them during lectures.
Exam
Information about date and time for the oral exam is distributed vi e-mail. Information about rooms will appear here later.
You can choose if you want to prepare a 12-15 minutes mini-presentation (no slides/computer, just use the blackboard and a manuscript). If you choose this option, you will asked to talk about one of the three topics below. We will throw a dice to decide which, so if you choose this option, you must be prepared to talk about all of them.
Note that you can also choose to not prepare and give a mini-presentation, and just have a "usual" oral exam instead.
The total exam-time will be the same independent of your choice, about 40-45 minutes.
Topic I: Almost split sequencs: What are they, and why do they exist. (Sketch the main steps in the existence theorem).
Topic II: AR-quivers: What are they, and how can they be computed for "nice" algebras of finite type (explain and illustrate the knitting technique on a small example).
Topic III: Nakayama algebra: What can we say about their module categories and in particular the almost split sequences and the AR-quiver of such algebras.
Notes
| Notes | Topic | Reference | |
|---|---|---|---|
| January 9 | Lecture 1 | (Path) algebras | AC-Chapter I |
| January 13 | Lecture 2 | (Path) algebras | AC-Chapter I |
| January 17 | Lecture 3 | Modules, Representations, length, KS-theorem | AC-Chapter I |
| January 20 | Lecture 4 | Radical, projectives, duality | AC-Chapter I |
| January 24 | Lecture 5 | Injectives, Nakayama algebras | AC-Chapter I |
| January 31 | Lecture 6 | Nakayama algebras | AC-Chapter I |
| February 3 | Lecture 7 | Hereditary algebras, Almost split sequences | AC-Chapter I, II |
| February 7 | Exercises 1 | Some exercises (from the notes + extra) | |
| February 10 | Lecture 8 | The radical of a module module category,irreducible maps | AC-Chapter II |
| February 14 | Lecture 9 | Irreducible maps | AC-Chapter II |
| February 17 | Lecture 10 | Minimal maps, almost split maps | AC-Chapter II |
| February 21 | CANCELLED | ||
| February 24 | Lecture 11 | Irreducible and almost split maps | AC-Chapter II |
| February 28 | Lecture 12 | Almost split sequences and the transpose | AC-Chapter II/III |
| March 3 | Lecture 13 | Functoriality of the AR-translation | AC-Chapter III |
| March 7 | Lecture 14 | The Auslander-Reiten formula | AC-Chapter III |
| March 10 | Lecture 15 | Existence of almost split sequences | AC-Chapter III |
| NO LECTURES MARCH 14-24 | Work with exercise set II + exercises from the lectures | ||
| March 28 | Exercises 2 | Exercise set II | AC-Chapter III |
| March 31 | Lecture 16 | Existence of almost split sequences cont. | AC-Chapter III |
| April 3 | Lecture 17 | The AR-quiver | AC-Chapter IV |
| April 4 | Lecture 18 | Knitting AR-quivers | AC-Chapter IV |
| April 7 | Lecture 19 | Finite type algebras (Auslanders theorem) | AC-Chapter VI |
| April 11 | Exercises 3 | Exercise set III | |
| April 24 | Lecture 20 | Tilting theory | AC-Chapter V |
| April 28 | Lecture 21 | tau-tilting theory | Expository paper |
| May 2 | CANCELLED |
The content of the course is what will presented during lectures. The first part of the course is covered by the book
Ibrahim Assem and Falvio Coelho, Basic Representation Theory of Algebras
Other useful books:
Ibrahim Assem, Daniel Simson, and Andrzej Skowronski, Elements of the Representation Theory of Associative Algebras: Volume 1: Techniques of Representation Theory, London Mathematical Society Student Texts 65
Maurice Auslander, Idun Reiten, and Sverre O. Smalø, Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics 36
Michael Barot, Introduction to the Representation Theory of Algebras, Springer, available on SpringerLink (provided you are on or surf through campus)
Alexander Zimmermann, Representation Theory, A Homological Algebra Point of View, Springer, available on SpringerLink (provided you are on or surf through campus)