Ray categories

Content

One of the main references will be the article by U. Fischbacher

• Zur Kombinatorik der Algebren mit endlich vielen Idealen (J. Reine Angew. Math. 370 (1986), 192-213)

• C. Geiß/Diplomarbeit: Darstellungsendliche Algebren und multiplikative Basen
  (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 downloaded here.

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 course.

Further References

• 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

• K.Bongartz: Indecomposables live in all smaller lengths (arXiv)

Programme

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 V3-204.

• 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
  • Ray categories IV