Comodules over Coalgebras

The topic of the first part of this semester's seminar will be the structure and representation theory of coalgebras. Juan Cuadra has made up a program consisting of the following six talks:

Name

Title

Date

1. Humberto Alvarez Algebras and Coalgebras 04.11.2003
2. Philipp Fahr Modules and Comodules 04.11.2003
3. Dong Liu Structure Theory of Coalgebras and Comodules 11.11.2003
4. Rolf Farnsteiner Equivalences between categories of comodules 18.11.2003
5. Juan Cuadra Special Classes of Coalgebras, I 25.11.2003
6. Juan Cuadra Special Classes of Coalgebras, II 02.12.2003

1. Algebras and coalgebras

2. Modules and comodules

3. Structure theory of coalgebras and comodules

4. Equivalences between categories of comodules

5. Special classes of coalgebras

6. Kleiner-Reiten's characterization of categories having almost split sequences


References

[A] Abe: Hopf algebras. Cambridge Tracts in Mathematics (1977)
[CH]Chin: A brief introduction to coalgebra representation theory
[CH2]Chin: Hereditary coalgebras and path coalgebras. Comm. Algebra 30 (2002), 1829-1831
[CM]Chin, Montgomery: Basic coalgebras AMS/IP studies in Advanced Math. 4 (1997), 41-47
[C1]Cuadra: Notes on algebras and coalgebras
[CG]Cuadra, Gomez-Torrecillas: Idempotents and Morita-Takeuchi Theory. Comm. Algebra 30 (2002), 2405-2426
[CG2]Cuadra, Gomez-Torrecillas: Serial coalgebras. To appear in J. Pure Appl. Algebra
[D] Doi: Homological coalgebra. J. Math. Soc. Japan 33 (1981), 31-50
[GN]Gomez-Torrecillas, Nastasescu: Quasi-co-Frobenius coalgebras. J. Algebra 174 (1995), 909-923
[G] Green, J.A.: Locally finite representations. J.Algebra 41 (1976), 137-171
[KR]Kleiner, Reiten: Abelian categories, almost split sequences, and comodules. Preprint 2003
[T2]Larson, Taft: The algebraic structure of linearly recursive sequences under Hadamard product. Israel J. Math. 72 (1980), 118-132
[L] Lin: Semiperfect coalgebras. J. Algebra 49 (1977), 357-373
[M1]Montgomery: Hopf algebras and their actions on rings. CBMS 82 (1993)
[M2]Montgomery: Indecomposable coalgebras, simple comodules and pointed Hopf algebras. Proc.Amer.Math.Soc. 123 (1995), 2343-2351
[NTZ]Nastasescu, Torrecillas, Zhang: Hereditary coalgebras. Comm. Algebra 24 (1996), 1521-1528
[NS]Novak, Simson: Locally Dynkin quivers and hereditary coalgebras whose left comodules are direct sums of finite dimensional comodules. Comm Algebra 30 (2002), 455-476
[T1]Peterson, Taft: The Hopf algebra of linearly recursive sequences. Aequationes Math. 20. No 1 (1980), 1-17
[Si]Simson: On coalgebras ot tame comodule type. In: Representations of Algebras II. Beijing Normal University (2002).
[S] Sweedler: Hopf algebras. Benjamin (1969)
[T] Takeuchi: Morita Theorems for categories of comodules. J. Fac. Sci. Univ. Tokyo 24 (1977), 629-644
[W] Woodcock: Some categorial remarks on the representation theory of coalgebras. Comm. Algebra 25 (1997), 2775-2794

Ringel
Last modified: Tue Nov 25 12:44:26 CET 2003