``Representations of Algebras" reading seminar, Autumn 2010, Winter 2011

PDL C-36, Friday 3:30-5pm


Some references

 

[ARS]  M. Auslander, I. Reiten, S. Smalo, ``Representation Theory of Artin Algebras"

[ASS]  I. Assem, D. Simson, A. Skowronski, ``Elements of the Representation Theory of Associative Algebras, I: Techniques of Representation Theory"

[B]  D. J. Benson, ``Representations and Cohomology, I: Basic representation theory of finite groups and associative algebras"

[CB]  W. Crawley-Boevey, Lectures on Representations of Quivers

[RS] C. Ringel, J. SchröerRepresentation theory of Algebras I: Modules

[Y]  Y. Yoshino, ``Cohen-Macauley modules over Cohen-Macauley rings"

 

Link to introductory material in representation theory of algebras in Paderborn

Fall Quarter

·  October, 8. Organizational meeting. Introductory presentations by Paul and Julia.

·  October, 15. ``Quivers, path algebras, and their representations", Jim and Gautam. Jim's notes, Gautam’s notes

·  October, 22. ``Quivers with relations; from algebras to quivers", Cody and Xingting

·  October, 29. ``Quivers with relations; from algebras to quivers", Xingting finishing up and switching from right to left modules

·  November, 5. Homework Assignment: [ASS], II.4. N3, (c), (f), (h); N12, N15; 

Introduction to Auslander-Reiten theory: “Irreducible morphisms and Almost Split Sequences", Chris

·  November, further dates. Paul Smith. Notes to be posted

 

 

Winter Quarter

January 4, “Almost split sequences”, Chris, notes to be posted
January 11, Practice session for the “Algebraic Structures” class

January 18, Chris finishes, Cody starts
January 25, “Auslander-Reiten translate”, Cody
February 11, Cody finishes, Min Wu starts on Auslander-Reiten quivers
February 21 – end of quarter, “Auslander-Reiten quivers”, Min Wu

 

Spring Quarter

Paul Smith recommends these notes on AR theory
April 7, Guangbin’s oral exam, no seminar
April 14, 21, “Auslander-Reiten quivers”, Min Wu
April 28, May 5, Examples of AR quivers for some path algebras, everyone talked, Min Wu’s “guideline notes
May 12, 19, ``Functorial approach to AR theory”, Jim, notes
May 26, “Nakayama algebras”, Gautam, notes