On tubes for blocks of wild type

Karin Erdmann

Colloquium Mathematicae (1999)

  • Volume: 82, Issue: 2, page 261-270
  • ISSN: 0010-1354

Abstract

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We show that any block of a group algebra of some finite group which is of wild representation type has many families of stable tubes.

How to cite

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Erdmann, Karin. "On tubes for blocks of wild type." Colloquium Mathematicae 82.2 (1999): 261-270. <http://eudml.org/doc/210761>.

@article{Erdmann1999,
abstract = {We show that any block of a group algebra of some finite group which is of wild representation type has many families of stable tubes.},
author = {Erdmann, Karin},
journal = {Colloquium Mathematicae},
keywords = {wild representation type; defect groups; vertices; finite groups; wild blocks; group algebras; stable Auslander-Reiten quivers; tubes},
language = {eng},
number = {2},
pages = {261-270},
title = {On tubes for blocks of wild type},
url = {http://eudml.org/doc/210761},
volume = {82},
year = {1999},
}

TY - JOUR
AU - Erdmann, Karin
TI - On tubes for blocks of wild type
JO - Colloquium Mathematicae
PY - 1999
VL - 82
IS - 2
SP - 261
EP - 270
AB - We show that any block of a group algebra of some finite group which is of wild representation type has many families of stable tubes.
LA - eng
KW - wild representation type; defect groups; vertices; finite groups; wild blocks; group algebras; stable Auslander-Reiten quivers; tubes
UR - http://eudml.org/doc/210761
ER -

References

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  1. [1] J. L. Alperin and M. Broué, Local methods in block theory, Ann. of Math. 110 (1979), 143-157. Zbl0416.20006
  2. [2] M. Auslander, I. Reiten and S. Smalο, Representation Theory of Artin Algebras, Cambridge Stud. Adv. Math. 36, Cambridge Univ. Press, 1994. 
  3. [3] K. Erdmann, On modules with cyclic vertices in the Auslander-Reiten quiver, J. Algebra 104 (1986), 289-300. Zbl0602.20011
  4. [4] K. Erdmann, On the vertices of modules in the Auslander-Reiten quiver of p-groups, Math. Z. 203 (1990), 321-334. Zbl0664.20009
  5. [5] K. Erdmann, Blocks of Tame Representation Type and Related Algebras, Lecture Notes in Math. 1428, Springer, 1990. Zbl0696.20001
  6. [6] K. Erdmann, On Auslander-Reiten components for group algebras, J. Pure Appl. Algebra 104 (1995), 149-160. Zbl0839.20007
  7. [7] W. Feit, The Representation Theory of Finite Groups, North-Holland, 1982. Zbl0493.20007
  8. [8] J. A. Green, Functors on categories of finite group representations, J. Pure Appl. Algebra 37 (1985), 265-298. Zbl0567.20001
  9. [9] D. Happel, U. Preiser and C. M. Ringel, Vinberg’s characterization of Dynkin diagrams using subadditive functions with applications to DTr-periodic modules, in: Representation Theory II, Lecture Notes in Math. 832, Springer, 1981, 280-294. 
  10. [10] S. Kawata, Module correspondences in Auslander-Reiten quivers for finite groups, Osaka J. Math. 26 (1989), 671-678. Zbl0705.20009
  11. [11] P. Landrock, Finite Group Algebras and Their Modules, London Math. Soc. Lecture Note Ser. 84, Cambridge Univ. Press, 1984. Zbl0523.20001
  12. [12] I. Reiten and A. Skowroński, Sincere stable tubes, preprint (Bielefeld 99-011). 

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