On tubes for blocks of wild type

ArticleOriginal scientific text

Title

Authors ¹

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.

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