Non-orbicular modules for Galois coverings

Piotr Dowbor

Colloquium Mathematicae, Tome 89 (2001), p. 241-310 / Harvested from The Polish Digital Mathematics Library

Résumé

Given a group G of k-linear automorphisms of a locally bounded k-category R, the problem of existence and construction of non-orbicular indecomposable R/G-modules is studied. For a suitable finite sequence B of G-atoms with a common stabilizer H, a representation embedding $Φ^{B} : Iₙ - spr(H) → mod(R/G)$, which yields large families of non-orbicular indecomposable R/G-modules, is constructed (Theorem 3.1). It is proved that if a G-atom B with infinite cyclic stabilizer admits a non-trivial left Kan extension B̃ with the same stabilizer, then usually the subcategory of non-orbicular indecomposables in $mod_{B̃,B}(R/G)$ is wild (Theorem 4.1, also 4.5). The analogous problem for the case of different stabilizers is discussed in Theorem 5.5. It is also shown that if R is tame then B̃ ≃ B for any infinite G-atom B with $End_{R}(B)/J(End_{R}(B)) ≃ k$ (Theorem 7.1). For this purpose the techniques of neighbourhoods (Theorem 7.2) and extension embeddings for matrix rings (Theorem 6.3) are developed.

Détail

Publié le : 2001-01-01

Zbl 0997.16007

EUDML-ID : urn:eudml:doc:284031