Following the lecture series by D. Vossieck, we plan to study in
more detail the essential results on ray categories in the second week
of September (7.9. – 11.9.).
One of the main references will be the article by U. Fischbacher
- C. Geiß/Diplomarbeit: Darstellungsendliche Algebren und
(D. Vossieck has made some copies of the relevant part
of the thesis which are available at V5-222.)
D. Vossieck has outlined a plan for the reading course, anyone is
invited to take part and to give one of these lectures.
The plan can be
In addition, he will provide information concerning parallel developments,
in particular also on deviating use of terminology.
Note that we have shifted the final lectures of his survey on the use and
the importance of ray categories, which he wanted to give at the end of
the summer term. They will be presented as an addition to this reading
- R. Bautista: On algebras of strongly unbounded representation
type, Comment. Math. Helv. 60 (1985), 392-399
- R. Bautista, P. Gabriel, A.V. Roiter,
L. Salmerón: Representation-finite algebras and multiplicative
bases, Invent. Math. 81 (1985), 217-285
- K. Bongartz: A criterion for finite representation type, Math.
Ann. 269 (1984), 1-12
- K. Bongartz: Critical simply connected algebras, Manuscr. Math.
46 (1984), 117-136
- K. Bongartz: Indecomposables are standard, Comment. Math. Helv.
60 (1985), 400-410
- O. Bretscher, P. Gabriel: The
standard form of a representation finite algebra, Bull. Soc. Math. France
111 (1983), 21-40
- O. Bretscher, G. Todorov: On a theorem of Nazarova and
Roiter, Proc. ICRA IV, Lecture Notes 1177 (1986), 50-54
- P. Gabriel, A.V. Roiter: Representations of
finite-dimensional algebras, Vol. 73 of the encyclopaedia of Math.
Sciences (1992), 1-177
Indecomposables live in
all smaller lengths (arXiv)
We will start with the reading course which will take place
during the first three days of the week. All talks will be held in
Finally, on Friday, 11 September, D. Vossieck will give the fourth part
of his lecture series on ray categories (which he started in the summer
- Monday, 7 September: in the afternoon, starting at 13:15
- Invariance of the fundamental group under reduction – D. Vossieck
- Tackles – A. Beineke
- Tuesday, 8 September: in the afternoon, starting at 13:15
- Reduction lemma – N. Mahrt
- Reducing filtrations, freeness of the fundamental group – D. Vossieck
- Roiter's vanishing theorem – A. Holtmann
- Wednesday, 9 September: in the afternoon, starting at 13:15
- Interval-finiteness: preparation – D. Kussin
- Interval-finiteness: conclusion – G. Bobiński
- Friday, 11 September: in the afternoon, starting at 13:15, V3-204
Last modified: Fri Aug 28 13:22:10 CEST 2009