Representation Theory of finite dimensional Algebras
This term, Wintersemester 2007, we offer the "Seminar für
Examenskandidaten / Diplomandenseminar",
which has a similar
structure as the previous Studygroup meetings.
Organisation:
| Who: | People interested in representation theory of algebras. Especially for Diplom/Master candidates and PhD-students. |
| What: | Representation theory of finite dimensional algebras, discussion of papers and different topics. |
| When: | Fridays 8:30-10 am |
| Where: | Room V4-116, Faculty of Mathematics |
| How: | Participants will present prepared material like a section of a book or part of a paper. It is hoped that each week someone else of the group will give a talk. Talks are usually given in English, exceptions can be made. The format is very informal and everyone is welcome to ask many questions during the session. |
| Questions: | Contact one of the organisers:
Claus
Ringel, Philipp
Fahr. |
This term, we will continue to discuss the list of all sincere simply-connected algebras, Rogat-Tesche (From: SFB 343, Ergänzungsreihe 93-005 (1993). You can download it on the LISTS-Page of FDLIST.
For a useful list of papers and books about representation theory of finite dimensional algebras, see the Algebra and Representation Theory in Bonn (ART) webpage at the University of Bonn. This is maintained by Jan Schröer.
Literature:
Books:
- Elements of the Representation Theory of Associative Algebras. I. Assem, A. Skowronski, D. Simson, 2006
- Tame Algebras and Integral Quadratic Forms (1984): Claus Michael Ringel; Springer Lecture Notes 1099; Chapters 1-3.
- Triangulated Categories in the Representation Theory of finite dimensional Algebras (1988): Dieter Happel.
- Representation Theory of Artin Algebras (1995): M. Auslander, I. Reiten, S. Smaloe; Important parts in the first eight chapters. Chapters 7 and 8 in detail.
- Lectures on Representations of Quivers: William Crawley-Boevey; We will cover whatever is still needed. (Done by Philipp Fahr)
- More Lectures on Representations of Quivers (1992): William Crawley-Boevey; Sections 1-4. (Done by Philipp Fahr)
- Coxeter Functors and Gabriel's Theorem (1972): I.N. Bernstein, I.M. Gel'fand, V.A. Ponomarev. (Done by Chen Bo)
- Indecomposable representations of graphs and algebras (1976): Vlastimil Dlab, Claus Michael Ringel; AMS Memoirs 173. (Done by Philipp Fahr)
- Representations of K-Species and Bimodules (1976): Claus Michael Ringel; Journal of Algebra 41, p.269-302. (Done by Philipp Fahr)
- Derived Categories, Derived Equivalences & Representation Theory (1998): Thorsten Holm. (Done by Liu Dong (C1&2) & Chen Bo (C3))
- Exceptional Objects in Hereditary Categories (1996): Claus Michael Ringel. Schofield induction. (Done by Chen Bo)
- The Gabriel-Roiter Measure (2003): Claus Michael Ringel.
- Recent Advances in the Representation Theory of finite dimensional Algebras (1991): Claus Michael Ringel.
- Algebra at the Turn of the Centuries (1999): Claus Michael Ringel.
- Combinatorial Representation Theory - History and Futture(2000): Claus Michael Ringel.
- Infinite Length Modules - Some Examples as Introduction
(2000): Claus Michael Ringel.
The following is a list of references of the material from which the topics of the talks were taken in the past:
Wildness:
- Otto Kerner: Representations of Wild Quivers, 1996.
- Otto Kerner: Basic results on wild hereditary algebras, 1998.
- William Crawley-Boevey, Otto Kerner: A functor between categories of regular modules for wild hereditary algebras, 1993.
- Tilting theory - An Introduction (1990): Ibrahim Assem. Topics in Algebra, Banach Center Publications (Vol. 26, Part 1, p.127-180).
- Tilted algebras (1981): K. Bongartz. Lecture Notes in Mathematics 903, Springer.
- Tilted Algebras (1982): Dieter Happel, Claus Michael Ringel; Transactions AMS 274.
Derived Categories:
- Derived Categories, Derived Equivalences & Representation Theory (1998): Thorsten Holm. (Done by Liu Dong (C1&2) & Chen Bo (C3)).
- Introduction to Abelian and Derived Categories: Bernhard Keller.
- Triangulated Categories in the Representation Theory of finite dimensional Algebras (1988): Dieter Happel.
- Algebra VIII: Representations of Finite-Dimensional
Algebras
(1992): P. Gabriel, A.V. Roiter; Chapter 12: Derivation and Tilting by
B. Keller.
List of talks:
| • | 19.9.2005: | Philipp Fahr: Cluster Categories. |
| • | 12.7.2005: | Chen Bo: Representations of Wild Quivers (VIII) |
| • | 5.7.2005: | Dorothea Jolk: Representations of Wild Quivers (VII) |
| • | 28.6.2005: | Andre Beineke: Representations of Wild Quivers (VI) |
| • | 14.6.2005: | Philipp Fahr: Examples of CB-Kerner-functors (4). |
| • | 7.6.2005: | Philipp Fahr: Representations of Wild Quivers (V). |
| • | 31.5.2005: | Yitao Wu: CB-Kerner-functors (3). |
| • | 24.5.2005: | Yitao Wu: CB-Kerner-functors (2). |
| • | 17.5.2005: | Chen Bo: Introduction to CB-Kerner-functors (1). |
| • | 10.5.2005: | Philipp Fahr: Representations of Wild Quivers (IV). |
| • | 3.5.2005: | Philipp Fahr: Representations of Wild Quivers (III). |
| • | 26.4.2005: | Philipp Fahr: Representations of Wild Quivers (II). |
| • | 19.4.2005: | Yitao Wu: Representations of Wild Quivers (I). |
| • | 11.4.2005: | Discussion of papers on wild algebras and regular modules for reading later in the Semester. |
| • | 12.1.2005: | Philipp Fahr: Practical Example - Introduction to Tilting Theory (5) |
| • | 5.1.2005: | Philipp Fahr: Brenner-Butler Theorem - Introduction to Tilting Theory (4) |
| • | 22.12.2004: | Chen Bo: (Partial) Tilting Modules and the AR-Quiver - Introduction to Tilting Theory (3) |
| • | 15.12.2004: | Andre Beineke: Torsion Theory - Introduction to Tilting Theory (2) |
| • | 8.12.2004: | Andre Beineke: Almost split sequences & Torsion Theory - Introduction to Tilting Theory (1) |
| • | 1.12.2004: | Philipp Fahr: K-Species and some more Representation Theory. (II) |
| • | 24.11.2004: | Philipp Fahr: Revision of Representation Theory and introduction of K-Species. (I) |
| • | 17.11.2004: | Discussion of papers on Tilting Theory for reading later in the Semester. |
| • | 20.07.2004: | Philipp Fahr: Overview on the finitistic global dimension conjecture. |
| • | 6.07.2004: | Chen Bo: Introduction to Ringel-Hall Algebras. |
| • | 29.06.2004: | Andre Beineke: The category of good modules over a quasi-hereditary algebra has almost split sequences. |
| • | 15.06.2004: | Philipp Fahr: Gabriel-Roiter-comeasure and Rhombic picture. (6) |
| • | 8.06.2004: | Philipp Fahr: Proof of "Classification Theorem 1" - Take-off part. (5) |
| • | 25.05.2004: | Philipp Fahr: Report on First Brauer-Thrall Conjecture with some history and Auslander's proof. (4) |
| • | 18.05.2004: | Philipp Fahr: 'Main Section' of the Gabriel-Roiter Measure paper. (3) |
| • | 4.05.2004: | Chen Bo: Proof and Corollaries of the 'Main Property' of the Gabriel-Roiter Measure. (2) |
| • | 27.04.2004: | Philipp Fahr: Start on the Gabriel-Roiter-Measure. Definitions and basic properties. (1) |
| • | 13.04.2004: | Chen Bo: Schofield Induction (Exceptional Objects in
Hereditary Categories - III - final) . Philipp Fahr: Introduction to Schur Algebras and revision of Coalgebras. |
| • | 6.04.2004: | Chen Bo: Schofield Induction (Exceptional Objects in
Hereditary Categories - II) . Philipp Fahr: Quasi-serial components of AR-quivers. |
| • | 23.03.2004: | Angela Holtmann: Knitting of preprojective components
of AR-Quivers. Chen Bo: Schofield Induction (Exceptional Objects in Hereditary Categories - I) . |
| • | 16.03.2004: | Philipp Fahr: Introduction to and Properties of Morita Equivalences. |
| • | 9.03.2004: | Chen Bo: Derived Categories, Derived Equivalences and
Representation Theory (4 - final). Philipp Fahr: Overview of Auslander-Reiten-Theory. |
| • | 2.03.2004: | Philipp Fahr: Indecomposable representations of graphs
and algebras (III - final). Chen Bo: Derived Categories, Derived Equivalences and Representation Theory (3). |
| • | 24.02.2004: | Liu Dong: Introduction to Triangulated Categories -
Derived Categories, Derived Equivalences and Representation Theory (2). Humberto Alvarez: Some properties of the radical. |
| • | 6.02.2004: | Philipp Fahr: Representation type: wild and strictly
wild & examples. |
| • | 30.01.2004: | Martin Zimniak: Derived Categories, Derived
Equivalences and Representation
Theory (1). Philipp Fahr: Indecomposable representations of graphs and algebras (II). |
| • | 23.01.2004: | Humberto Alvarez: Right and left minimal morphisms. |
| • | 16.01.2004: | Liu Dong: Triangular matrix rings (2 - final). Philipp Fahr: Indecomposable representations of graphs and algebras (I). |
| • | 9.01.2004: | Liu Dong: One point extensions, more on Triangular matrix rings and Group algebras (1). |
| • | 19.12.2003: | Chen Bo: Algebraic Varieties needed for the proof of
Gabriel's Theorem. Chen Bo: Coxeter Functors and Gabriel's Theorem (III - final). |
| • | 5.12.2003: | Chen Bo: Coxeter Functors and Gabriel's Theorem (II). |
| • | 4.12.2003: | Philipp Fahr: Quivers and their representations, Path algebras and more. |
| • | 28.11.2003: | Humberto Alvarez: Homological algebra. |
| • | 21.11.2003: | Philipp Fahr: Blocks and Projectivization. Chen Bo: Coxeter Functors and Gabriel's Theorem (I). |
| • | 14.11.2003: | Humberto Alvarez: Finite length modules &
Jordan-Hoelder Theorem. Philipp Fahr: Artin algebras and additive R-categories. |
| • | 7.11.2003: | First meeting of the Studygroup BIREP. Organisation of talks and topics. |
Last modified: October 2007