BIREP — Representations of finite dimensional algebras in Bielefeld

• BIREP
• Faculty of Mathematics
• Bielefeld University

 

The Algebra Seminar (Seminar on Representation Theory) (eKVV: 241442)

Seminar in english, summer term 2019 (2 SWS)
Organizer: Dr. Julia Sauter
Termin:

• Wednesday, 10.15-11.45h in X-E0-208

Termine im SoSe 19:

• April 17: Auslander algebras - usual [A], higher [I] and relative [MS], Julia Sauter
• April 24: Coproducts of rings, Johannes Krah
• May 8: dg algebras [K], [O], Biao Ma
• May 15: A-infinity algebras, David Fernandez
• May 22: Quasi-hereditary algebras, Manuel Flores
• May 29: Tubular algebras, Sebastian Eckert
• June 5: Tubes, Andrew Hubery
• June 12: --
• June 19: Diagram algebras, William Crawley-Boevey
• June 26: Group rings [Li1], [Li2], Baptiste Rognerud
• July 3: Preprojective algebras, Yuta Kimura
• July 10: -- (talk is cancelled)

Description: The Algebra Seminar
This is a working seminar of the Birep group which is open to everybody interested. The aim of the seminar is to visit a variety of different algebras and explain their history, interesting features and results. This means that the individual topics are independent and can vary substantially in the level of required prerequisites. We are not attempting to structure these different algebras (there might even be overlapp between them, some might be infinite-dimensional) but to give a taste of the versatility and to widen our horizon. Here are some suggestions (made by members of the Birep group) but any other suggestion is very welcome (for example have a look at Jan Schroer's FD atlas).

• Representation-finite algebras:
  
  • Nakayama algebras
  • Representation-finite selfinjective algebras [R]
• Tame algebras
  • Tame concealed algebras
  • Gentle algebras
  • Derived discrete algebras
  • string algebras
• Gorenstein rings
  • Self-injective algebras
    • Group rings [Li1], [Li2]
    • Representation-finite selfinjective algebras [R]
    • Brauer graph algebras
    • Preprojective algebras of Dynkin type
    • Repetitive Algebras
  • Gentle algebras
  • Algebras from surface triangulations
  • Skew group rings [RR],[L]
  • Complete intersections, in particular hypersurface singularities
• Algebras appearing in higher AR-theory
  • Higher Nakayama algebras
  • Higher preprojective algebras
  • Higher Auslander algebras [I]
  • Higher zigzag algebras, [G]
• (Quasi-)Tilted algebras
  • Canonical algebras
• Quasi-hereditary algebras
  • Schur algebras
  • Auslander algebras [A]
• Jacobians for quivers with potential
• Dimer models
• Calabi-Yau algebras
• tubular algebras
• wild algebras (?)
• Koszul algebras
• radical square zero algebras
• Tensor algebras
• Multiserial algebras

Literatur:

• [A] Maurice Auslander: Representation dimension of artin algebras, Selected works of Maurice Auslander. Part 1 (1999)
• [G] Joseph Grant: Higher zigzag algebras arxiv
• [I] Osamu Iyama: Auslander correspondence, Adv. Math. 210 (2007) no 1, 51-82
• [K] Bernhard Keller: On differential graded categories, Proc. of the ICM (2006)
• [L] Helmut Lenzing: Polyhedral groups and the geometry of tame hereditary artin algebras (unpublished lecture notes)
• [Li1] Markus Linckelmann: The Block Theory of Finite Group Algebras vol 1(LMS). Cambridge University Press (2018).
• [Li2] Markus Linckelmann:. The Block Theory of Finite Group Algebras vol 2 (LMS). Cambridge University Press (2018).
• [MS] Biao Ma, Julia Sauter: On faithfully balanced modules, F-cotilting and F-Auslander algebras, arxiv
• [O] Steffen Oppermann: Quivers for siliting mutation, Adv. in Math.(2017)
• [RR] Idun Reiten, Christine Riedtmann: Skew group algebras in the representation theory of Artin algebras, J. Algebra 92 (1985), no. 1, 224–282.
• [R] Christine Riedtmann: Algebren, Darstellungskoecher und zurueck, Comment. Math. Helv. 55 (1980), no. 2, p.199–224.