BIREP-Seminar

Reading course: Representation dimension

Continuation: SS 2008

[1] S. Oppermann: A lower bound for the representation dimension of kC_pⁿ
pdf-file
[2] P. Bergh: Representation dimension and finitely generated cohomology
pdf-file
[3] P. Bergh, S. Oppermann: Complexity and the dimension of a triangulated category
pdf-file
[4] S. Oppermann: Lower bounds for Auslander's representation dimension
pdf-file

• 11. April
  • Ringel: Iyama's Finiteness theorem vis strongly quasi-hereditary algebras.
  • Farnsteiner: Complexity and representation dimension [1,2]
• 18. April
  • Holtmann: Complexity and the dimension of a triangulated category I [3, pp.1-6]
  • Pucinskaite: Complexity and the dimension of a triangulated category II [3, pp.7-10]
  • Bois Dimensions and vanishing of extensions [4, parts 1,2]
• 25. April
  • Mahrt: Generic non-vanishing and lower bounds for dimensions [4, part 3]
  • Rosnau: Exterior algebras and truncated polynomial rings [4, parts 4,5]
  • Yao: Coverings [4, part 6]

WS 2007/08

This reading course will deal with some papers on the topic of Representation Dimension. The lectures are usually Fridays from 13:00 in T2-228.

21.12.2007	Ringel	The relevance
11.01.2008	Yao	Auslander algebras	(ARS)
11.01.2008	Pucinskaite	Representation dimension	(QMN)
18.01.2008	Rosnau	Rep dim and radicals	(Xi 2000, 338-342)
18.01.2008	Mahrt	Rep dim and global dim	(Xi 2000, 342-343)
25.01.2008	Beineke	Finiteness	(Iyama)
25.01.2008	Bobinski	Radical embeddings I	(EHIS, 159-167)
01.02.2008	Ringel	Radical embeddings II	(EHIS, 168-176)
01.02.2008	Holtmann	The dimension of a triang.cat.	(Rouquier, 357-362)
08.02.2008	Holtmann	The exterior algebra	(Rouquier, 362-367)

The papers to be discussed

• Xi: On the representation dimension of finite dimensional algebras. J.Algebra 226 (2000), 332-346.
• Xi: Representation dimension and quasi-hereditary algebras. Adv. Math. 168 (2002), 193-212.
• Erdmann-Holm-Iyama-Schröer: Radical embeddings and representation dimension. Adv. Math. 185 (2004) 159-177
• Iyama: Finiteness of representation dimension. Proc. Amer.Math.Soc. 131 (2002), 1011-1014.
• Rouquier: Representation dimension of exterior algebras. Inventiones math. 165 (2006), 357-367.

Surveys

• Artin algebras of dominant dimension ≥ 2.
  (Selected topics, 5.12.2007)
• The torsionless modules of an artin algebra
  (Selected topics, 9.1.2008)