Non-orbicular modules for Galois coverings

• Autorzy: Piotr Dowbor
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16G60: Representation type (finite, tame, wild, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 89
• Numer: 2
• Strony: 241-310

Daty

wydano

2001

Twórcy

autor

Piotr Dowbor

• Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Identyfikatory

DOI

10.4064/cm89-2-9